What is the LCM of 34 and 102 - Find out answer step by step

What is LCM?

In mathematics, least common multiple, which is ordinarily reffered to as LCM is characterized as the smallest non-zero number which is divisible by both given numbers 34 and 102.

Properties of LCM

LCM follows associative property, that means LCM(34, 102) = LCM(102, 34).
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 34 and 102 is 102, where 34 and 102 are less than 102.
The LCM of two or more prime numbers is their product.

Steps to find lcm of 34 and 102 by Listing Method

Find some first multiples of 34 and 102.
Find the least common multiple, and read off the answer!

Example: Find lcm of 34 and 102 by Listing Method

Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340, 374, 408, 442, 476, 510, 544, 578, 612, 646, 680, 714, 748, 782, 816, 850, 884, 918, 952, 986, 1020, 1054, 1088, 1122, 1156, 1190, 1224, 1258, 1292, 1326, 1360, 1394, 1428, 1462, 1496, 1530, 1564, 1598, 1632, 1666, 1700, 1734, 1768, 1802, 1836, 1870, 1904, 1938, 1972, 2006, 2040, 2074, 2108, 2142, 2176, 2210, 2244, 2278, 2312, 2346, 2380, 2414, 2448, 2482, 2516, 2550, 2584, 2618, 2652, 2686, 2720, 2754, 2788, 2822, 2856, 2890, 2924, 2958, 2992, 3026, 3060, 3094, 3128, 3162, 3196, 3230, 3264, 3298, 3332, 3366, 3400, 3434, 3468
Multiples of 102: 102, 204, 306, 408, 510, 612, 714, 816, 918, 1020, 1122, 1224, 1326, 1428, 1530, 1632, 1734, 1836, 1938, 2040, 2142, 2244, 2346, 2448, 2550, 2652, 2754, 2856, 2958, 3060, 3162, 3264, 3366, 3468

Hence, LCM of 34 and 102 is 102.

Steps to find LCM of 34 and 102 by Common Division Method

Find all the prime numbers that would divide 34 and 102 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 34 and 102 by Common Division Method

2	34 102
3	17 51
17	17 17
	1 1

Hence, LCM of 34 and 102 is 2 x 3 x 17 = 102.

Steps to find lcm of 34 and 102 by Formula

The formula for LCM is LCM (34, 102) = (34 x 102) / GCF (34, 102)
Apply the formula, and read off the answer!

Example: Find lcm of 34 and 102 by Formula

GCF of 34 and 102 = 34
LCM of 34 and 102 = (34 x 102) / 34
=> 3468 / 34

Hence, LCM of 34 and 102 is 102.

Examples

A shopkeeper sells candies in packet of 34 and chocolates in packet of 102. 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 34 and 102.
So, LCM of 34 and 102 is 102.

Both the cricket team and the rugby team had games, today. The cricket team plays every 34 days and the basketball team plays every 102 days. When will both teams have games on the same day again?

Given that the cricket team plays every 34 days and the basketball team plays every 102 days, so for finding the next time when both teams will play again we need to find the LCM of 34 and 102.
So, LCM of 34 and 102 is 102.

Steve spends 34 dollars every day while George spends 102 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 34 and 102.
So, LCM of 34 and 102 is 102.

Sammy's company prints 34 textbooks at a time. Daniel's company prints textbooks in sets of 102 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 34 and 102.
So, LCM of 34 and 102 is 102.

Ariel exercises every 34 days and Rubel every 102 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 34 and 102 is 102.

Find the least common multiple of 34 and 102.

Least common multiple of 34 and 102 is 102.

Find the least number which is exactly divisible by 34 and 102.

Least number which is exactly divisible by 34 and 102 is 102.

What is LCM of 34 and 102?

How to find lcm of two numbers

What is LCM?

Properties of LCM

Steps to find lcm of 34 and 102 by Listing Method

Example: Find lcm of 34 and 102 by Listing Method

Steps to find LCM of 34 and 102 by Common Division Method

Example: Find lcm of 34 and 102 by Common Division Method

Steps to find lcm of 34 and 102 by Formula

Example: Find lcm of 34 and 102 by Formula

Examples

What is LCM of 34 and 102?

How to find lcm of two numbers

What is LCM?

Properties of LCM

Steps to find lcm of 34 and 102 by Listing Method

Example: Find lcm of 34 and 102 by Listing Method

Steps to find LCM of 34 and 102 by Common Division Method

Example: Find lcm of 34 and 102 by Common Division Method

Steps to find lcm of 34 and 102 by Formula

Example: Find lcm of 34 and 102 by Formula

Examples

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