help me find the LCM for 112 & 96 would 28 be right?

Question

also on 56 & 96 find LCM of each group of expressions
60,80,50 also.......
I would appreciate any help..........thanks

Answer 1

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 *multiple* is 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 *multiples* would 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

Answer 2

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.

Answer 3

The LCM of 112 and 96 is 672. 112 = 2^4*7, and 96 is 2^5*3. The lowest common multiple of those is 2^5*7*3, or 672.

56 = 2^3*7, 96 = 2^5*3; LCM is also 2^5*3*7, or 672.

60 = 2^2*3*5, 80 = 2^4*5, 50 = 2*5^2; LCM = 2^4*3*5^2 or 1200.

Answer 4

112 = 2*2*2*2*7
96 = 2*2*2*2*2*3
LCM = 2*2*2*2*2*3*7 = 7*96 = 672
GCF = 16

56 = 2*2*2*7
96 = 2*2*2*2*2*3
LCM = 2*2*2*2*2*3*7 = 7*96 = 672 (again)

60 = 2*2*3*5
80 = 2*2*2*2*5
50 = 2*5*5
LCM = 2*2*2*2*3*5*5 = 15*80 = 1,200

The rest is lost because Answers editor ......'s if your string is too long.

Answer 5

112=2^4*7
96 =2^4*3
LCM=2^4*7*3=336

56=2^3*7
96=2^4*3
LCM=2^4*3*7=336