## Least common multiples of two- digit numbers. I need two examples. SHOW WORK

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Least common multiples of two- digit numbers. I need two examples. SHOW WORK

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1 month 2021-08-07T20:03:28+00:00 1 Answers 3 views 0

1. 9514 1404 393

• LCM(21, 51) = 357
• LCM(42, 90) = 630

Step-by-step explanation:

For a pair of numbers, I find it convenient to think in terms of factors unique to the number, and factors shared with the other number.

Consider the numbers 21 and 51, for example.

21 = 3·7

51 = 3·17

The factor 3 is shared by both numbers. The factors 7 and 17 are unique to one number or the other.

If we group these factors like this …

(factors unique to 1 [ shared factors ) factors unique to 2]

= (7 [3 ) 17]

The numbers in ( ) parentheses are the factors of 21, and the numbers in [ ] brackets are the factors of 51.

The LCM (least common multiple) is the product of the factors in those brackets:

LCM(21, 51) = 7 × 3 × 17 = 357

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The unique factors of the numbers don’t have to be prime (as in the above example); they just cannot be shared. Here’s another example for the numbers 42 and 90

(7 [ 3·2 ) 3·5 ] = (7 [ 6 ) 15] . . . . factors of (42) and 

Then the LCM is …

LCM(42, 90) = 7 × 6 × 15 = 630

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