also on 56 & 96 find LCM of each group of expressions

60,80,50 also.......

I would appreciate any help..........thanks

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also on 56 & 96 find LCM of each group of expressions

60,80,50 also.......

I would appreciate any help..........thanks

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## Answers (2)

Remember what a multiple is:

112, 224, 336, 448, 560, 672, etc. are multiples of 112

96, 192, 288, 384, 480, 576, 672, etc. are multiples of 96

The lowest common

multipleis 672.To figure this, calculate the prime factors:

112 / 2 = 56

56 / 2 = 28

28 / 2 = 14

14 / 2 = 7

7 / 7 = 1

112 = 2 x 2 x 2 x 2 x 7

96 / 2 = 48

48 / 2 = 24

24 / 2 = 12

12 / 2 = 6

6 / 2 = 3

3 / 3 = 1

96 = 2 x 2 x 2 x 2 x 2 x 3

The common

multipleswould be the number that includes all these factors (2 x 2 x 2 x 2 x 2 x 3 x 7 = 672).LCM (112, 96) = 672

Don't confuse this with greatest common factor. This would be a number smaller than both. While the lowest common multiple is a number bigger than both.

LCM (56, 96):

56 / 2 = 28

28 / 2 = 14

14 / 2 = 7

7 / 7 = 1

96 = 2 x 2 x 2 x 2 x 2 x 3

56 = 2 x 2 x 2 x 7

LCM (96, 56) = 2 x 2 x 2 x 2 x 2 x 3 x 7 = 672

And your last problem:

60 = 2 x 2 x 3 x 5

80 = 2 x 2 x 2 x 2 x 5

50 = 2 x 5 x 5

Altogether you need four twos (2 x 2 x 2 x 2) a three (3) and two fives (5 x 5):

LCM (60, 80, 50) = 2 x 2 x 2 x 2 x 3 x 5 x 5 = 1200

So in summary:

LCM (112, 96) = 672

LCM (56, 96) = 672

LCM (60, 80, 50) = 1200

The LCM is the Least Common Multiple. This is easily confused with the GCF, the Greatest Common Factor. The LCM is the smallest number that is a multiple of both numbers. The LCM must be at least equal to the larger of the numbers.

28 is the GCF for 112 & 96.

First, get the prime factorizations of each number.

112 = 2^4 * 7

96 = 2^5 * 3

80 = 2^4 * 5

60 = 2^2 * 3 * 5

56 = 2^3 * 7

50 = 2 * 5^2

To find the LCM, compare the prime factorizations. For 112 and 96,

112 = 2^4 * 7

96 = 2^5 * 3

The LCM for them is 2^5 * 3 * 7, or 672.

For a more detailed explanation, check out the link below.

Reference:purplemath.com/modules/lcm_gcf.htm