What is the LCM of 78 and 140 - Find out answer step by step

What does LCM mean in mathematics?

The least common multiple or LCM of two numbers 78 and 140 is defined as the smallest positive integer which is divisible by both of them. It is represented by LCM(78, 140).

Properties of LCM

LCM follows associative property, that means LCM(78, 140) = LCM(140, 78).
LCM follows commutative property, which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
LCM follows distributive property, which means LCM(ab, bc, ad) = d * LCM(x, y, z).
The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 78 and 140 is 5460, where 78 and 140 are less than 5460.
The LCM of two or more prime numbers is their product.

Steps to find lcm of 78 and 140 by Listing Method

Find some first multiples of 78 and 140.
Find the least common multiple, and read off the answer!

Example: Find lcm of 78 and 140 by Listing Method

Multiples of 78: 78, 156, 234, 312, 390, 468, 546, 624, 702, 780, 858, 936, 1014, 1092, 1170, 1248, 1326, 1404, 1482, 1560, 1638, 1716, 1794, 1872, 1950, 2028, 2106, 2184, 2262, 2340, 2418, 2496, 2574, 2652, 2730, 2808, 2886, 2964, 3042, 3120, 3198, 3276, 3354, 3432, 3510, 3588, 3666, 3744, 3822, 3900, 3978, 4056, 4134, 4212, 4290, 4368, 4446, 4524, 4602, 4680, 4758, 4836, 4914, 4992, 5070, 5148, 5226, 5304, 5382, 5460, 5538, 5616, 5694, 5772, 5850, 5928, 6006, 6084, 6162, 6240, 6318, 6396, 6474, 6552, 6630, 6708, 6786, 6864, 6942, 7020, 7098, 7176, 7254, 7332, 7410, 7488, 7566, 7644, 7722, 7800, 7878, 7956, 8034, 8112, 8190, 8268, 8346, 8424, 8502, 8580, 8658, 8736, 8814, 8892, 8970, 9048, 9126, 9204, 9282, 9360, 9438, 9516, 9594, 9672, 9750, 9828, 9906, 9984, 10062, 10140, 10218, 10296, 10374, 10452, 10530, 10608, 10686, 10764, 10842, 10920
Multiples of 140: 140, 280, 420, 560, 700, 840, 980, 1120, 1260, 1400, 1540, 1680, 1820, 1960, 2100, 2240, 2380, 2520, 2660, 2800, 2940, 3080, 3220, 3360, 3500, 3640, 3780, 3920, 4060, 4200, 4340, 4480, 4620, 4760, 4900, 5040, 5180, 5320, 5460, 5600, 5740, 5880, 6020, 6160, 6300, 6440, 6580, 6720, 6860, 7000, 7140, 7280, 7420, 7560, 7700, 7840, 7980, 8120, 8260, 8400, 8540, 8680, 8820, 8960, 9100, 9240, 9380, 9520, 9660, 9800, 9940, 10080, 10220, 10360, 10500, 10640, 10780, 10920

Hence, LCM of 78 and 140 is 5460.

Steps to find LCM of 78 and 140 by Common Division Method

Find all the prime numbers that would divide 78 and 140 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 78 and 140 by Common Division Method

2	78 140
2	39 70
3	39 35
5	13 35
7	13 7
13	13 1
	1 1

Hence, LCM of 78 and 140 is 2 x 2 x 3 x 5 x 7 x 13 = 5460.

Steps to find lcm of 78 and 140 by Formula

The formula for LCM is LCM (78, 140) = (78 x 140) / GCF (78, 140)
Apply the formula, and read off the answer!

Example: Find lcm of 78 and 140 by Formula

GCF of 78 and 140 = 2
LCM of 78 and 140 = (78 x 140) / 2
=> 10920 / 2

Hence, LCM of 78 and 140 is 5460.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 78 and 140 minutes respectively to go round once. Find at what time they will run together?

Franky and Joy are running on a circular track. They take 78 and 140 minutes respectively to go round once. We need to find out at what time (minimum) they will run together again. For this we need to find the LCM of 78 and 140.
So, LCM of 78 and 140 is 5460.

A shopkeeper sells candies in packet of 78 and chocolates in packet of 140. What is the least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate?

The least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate we need to find the lcm of 78 and 140.
So, LCM of 78 and 140 is 5460.

Both the cricket team and the rugby team had games, today. The cricket team plays every 78 days and the basketball team plays every 140 days. When will both teams have games on the same day again?

Given that the cricket team plays every 78 days and the basketball team plays every 140 days, so for finding the next time when both teams will play again we need to find the LCM of 78 and 140.
So, LCM of 78 and 140 is 5460.

Freddy saves 78 dollars every day while Nikki saves 140 dollars every day. What is the least number of days it will take each person to save the same amount of money?

To find the least number of days that would be taken to be able to save the same amount of dollars we need to find the LCM of 78 and 140.
So, LCM of 78 and 140 is 5460.

Boxes that are 78 inches tall are being pilled next to boxes that are 140 inches tall. What is the least height in feet at which the two piles will be the same height?

To find the least height in feet at which the two piles will be at same height we will find LCM of 78 and 140.
So, LCM of 78 and 140 is 5460.

Sammy's company prints 78 textbooks at a time. Daniel's company prints textbooks in sets of 140 at a time. According to a survey done by a committee, both companies printed the same number of textbooks last year. Find the least number of books that each company would have printed.

To find the least number of textbooks that each company could have printed we need to find the LCM of 78 and 140.
So, LCM of 78 and 140 is 5460.

Ariel exercises every 78 days and Rubel every 140 days. They both excercised today. How many days will it be until they excercise together again?

The problem can be solved using LCM, because we are trying to figure out the least time until they excercise together again.
So, LCM of 78 and 140 is 5460.

What is LCM of 78 and 140?

How to find lcm of two numbers

What does LCM mean in mathematics?

Properties of LCM

Steps to find lcm of 78 and 140 by Listing Method

Example: Find lcm of 78 and 140 by Listing Method

Steps to find LCM of 78 and 140 by Common Division Method

Example: Find lcm of 78 and 140 by Common Division Method

Steps to find lcm of 78 and 140 by Formula

Example: Find lcm of 78 and 140 by Formula

Examples

What is LCM of 78 and 140?

How to find lcm of two numbers

What does LCM mean in mathematics?

Properties of LCM

Steps to find lcm of 78 and 140 by Listing Method

Example: Find lcm of 78 and 140 by Listing Method

Steps to find LCM of 78 and 140 by Common Division Method

Example: Find lcm of 78 and 140 by Common Division Method

Steps to find lcm of 78 and 140 by Formula

Example: Find lcm of 78 and 140 by Formula

Examples

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