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In Mathematics / Middle School | 2014-09-21

What is the least common multiple (LCM) of the following pairs of numbers?

A. 13 and 20
B. 11 and 13
C. 17 and 7
D. 17 and 8

Asked by oriellasatchell

Answer (3)

13 and 20 is 260 11 and 13 is 143,17 and 7 is 119, 17 and 8 is 136

Answered by vicky4life | 2024-06-10

The LCMs are as follows: LCM of 13 and 20 is 260, LCM of 11 and 13 is 143, LCM of 17 and 7 is 119, and LCM of 17 and 8 is 136. Each LCM can be found by listing and comparing the multiples of the two numbers until a common multiple is found.
Finding the Least Common Multiple (LCM)
The Least Common Multiple (LCM) of two numbers is the smallest positive integer that is a multiple of both numbers. Here's how to find the LCM of the given pairs of numbers:
LCM of 13 and 20

List the multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, ...
List the multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, ...

The smallest common multiple is 260.
Therefore, the LCM of 13 and 20 is 260.
LCM of 11 and 13

List the multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, ...
List the multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, ...

The smallest common multiple is 143.
Therefore, the LCM of 11 and 13 is 143.
LCM of 17 and 7

List the multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, ...

List the multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, ...


The smallest common multiple is 119.
Therefore, the LCM of 17 and 7 is 119.
LCM of 17 and 8

List the multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, 306, 323, ...
List the multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, ...

The smallest common multiple is 136.
Therefore, the LCM of 17 and 8 is 136.

Answered by EdwardRow | 2024-06-24

The LCMs of the numbers are as follows: 13 and 20 yield 260, 11 and 13 yield 143, 17 and 7 yield 119, and 17 and 8 yield 136.
;

Answered by EdwardRow | 2024-12-26

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