Question

LCM: 1) 36 , 58 and 68 2) 130 , 142 and 156​

Answer 1

Answer:

1). 17748

2). 55380

Step-by-step explanation:

1). List all prime factors for each number.

Prime Factorization of 36 is:

2 x 2 x 3 x 3  =>  22 x 32

Prime Factorization of 58 is:

2 x 29  =>  21 x 291

Prime Factorization of 68 is:

2 x 2 x 17  =>  22 x 171

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3, 3, 17, 29

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 x 3 x 17 x 29 = 17748

In exponential form:

LCM = $2^{2}$ x $3^{2}$ x $17^{1}$ x $29^{1}$ = 17748

LCM = 17748

Therefore,

LCM(36, 58, 68) = 17,748

2).List all prime factors for each number.

Prime Factorization of 130 is:

2 x 5 x 13  =>  21 x 51 x 131

Prime Factorization of 142 is:

2 x 71  =>  21 x 711

Prime Factorization of 156 is:

2 x 2 x 3 x 13  =>  22 x 31 x 131

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3, 5, 13, 71

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 x 5 x 13 x 71 = 55380

In exponential form:

LCM = $2^{2}$ x $3^{1}$ x $5^{1}$ x $13^{1}$ x $71^{1}$ = 55380

LCM = 55380

Therefore,

LCM(130, 142, 156) = 55,380

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hope it helps.