What is the LCM of 42 and 126 - Find out answer step by step

How do we define LCM?

LCM, abbreviation for least common multiple, is defined as the smallest number that is the product of two or more numbers 42 and 126

Properties of LCM

LCM follows associative property, that means LCM(42, 126) = LCM(126, 42).
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 42 and 126 is 126, where 42 and 126 are less than 126.
The LCM of two or more prime numbers is their product.

Steps to find lcm of 42 and 126 by Listing Method

Find some first multiples of 42 and 126.
Find the least common multiple, and read off the answer!

Example: Find lcm of 42 and 126 by Listing Method

Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504, 546, 588, 630, 672, 714, 756, 798, 840, 882, 924, 966, 1008, 1050, 1092, 1134, 1176, 1218, 1260, 1302, 1344, 1386, 1428, 1470, 1512, 1554, 1596, 1638, 1680, 1722, 1764, 1806, 1848, 1890, 1932, 1974, 2016, 2058, 2100, 2142, 2184, 2226, 2268, 2310, 2352, 2394, 2436, 2478, 2520, 2562, 2604, 2646, 2688, 2730, 2772, 2814, 2856, 2898, 2940, 2982, 3024, 3066, 3108, 3150, 3192, 3234, 3276, 3318, 3360, 3402, 3444, 3486, 3528, 3570, 3612, 3654, 3696, 3738, 3780, 3822, 3864, 3906, 3948, 3990, 4032, 4074, 4116, 4158, 4200, 4242, 4284, 4326, 4368, 4410, 4452, 4494, 4536, 4578, 4620, 4662, 4704, 4746, 4788, 4830, 4872, 4914, 4956, 4998, 5040, 5082, 5124, 5166, 5208, 5250, 5292
Multiples of 126: 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260, 1386, 1512, 1638, 1764, 1890, 2016, 2142, 2268, 2394, 2520, 2646, 2772, 2898, 3024, 3150, 3276, 3402, 3528, 3654, 3780, 3906, 4032, 4158, 4284, 4410, 4536, 4662, 4788, 4914, 5040, 5166, 5292

Hence, LCM of 42 and 126 is 126.

Steps to find LCM of 42 and 126 by Common Division Method

Find all the prime numbers that would divide 42 and 126 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 42 and 126 by Common Division Method

2	42 126
3	21 63
3	7 21
7	7 7
	1 1

Hence, LCM of 42 and 126 is 2 x 3 x 3 x 7 = 126.

Steps to find lcm of 42 and 126 by Formula

The formula for LCM is LCM (42, 126) = (42 x 126) / GCF (42, 126)
Apply the formula, and read off the answer!

Example: Find lcm of 42 and 126 by Formula

GCF of 42 and 126 = 42
LCM of 42 and 126 = (42 x 126) / 42
=> 5292 / 42

Hence, LCM of 42 and 126 is 126.

Examples

A shopkeeper sells candies in packet of 42 and chocolates in packet of 126. 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 42 and 126.
So, LCM of 42 and 126 is 126.

Both the cricket team and the rugby team had games, today. The cricket team plays every 42 days and the basketball team plays every 126 days. When will both teams have games on the same day again?

Given that the cricket team plays every 42 days and the basketball team plays every 126 days, so for finding the next time when both teams will play again we need to find the LCM of 42 and 126.
So, LCM of 42 and 126 is 126.

Steve spends 42 dollars every day while George spends 126 dollars every day. What is the least number of days it will take each person to spend the same amount of money?

To find the least number of days that would be taken to be able to spend the same amount of dollars we need to find the LCM of 42 and 126.
So, LCM of 42 and 126 is 126.

Sammy's company prints 42 textbooks at a time. Daniel's company prints textbooks in sets of 126 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 42 and 126.
So, LCM of 42 and 126 is 126.

Ariel exercises every 42 days and Rubel every 126 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 42 and 126 is 126.

Find the least common multiple of 42 and 126.

Least common multiple of 42 and 126 is 126.

Find the least number which is exactly divisible by 42 and 126.

Least number which is exactly divisible by 42 and 126 is 126.

What is LCM of 42 and 126?

How to find lcm of two numbers

How do we define LCM?

Properties of LCM

Steps to find lcm of 42 and 126 by Listing Method

Example: Find lcm of 42 and 126 by Listing Method

Steps to find LCM of 42 and 126 by Common Division Method

Example: Find lcm of 42 and 126 by Common Division Method

Steps to find lcm of 42 and 126 by Formula

Example: Find lcm of 42 and 126 by Formula

Examples

What is LCM of 42 and 126?

How to find lcm of two numbers

How do we define LCM?

Properties of LCM

Steps to find lcm of 42 and 126 by Listing Method

Example: Find lcm of 42 and 126 by Listing Method

Steps to find LCM of 42 and 126 by Common Division Method

Example: Find lcm of 42 and 126 by Common Division Method

Steps to find lcm of 42 and 126 by Formula

Example: Find lcm of 42 and 126 by Formula

Examples

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