Question

Find the LCM of the following numbers by prime factorization method. 39, 81,65,75​

Answer 1

Answer:

Step-by-step explanation:

The prime factors of 39 are 3 and 13.

The prime factors of 81 are 3, 3, 3 and 3.

The prime factors of 65 are 5 and 13.

The prime factors of 75 are 3, 5 and 5.

Determine the maximum number of times each prime factor (3, 5, 13) occurs in the factorization of the given numbers:

The prime factor 13 occurs one time, while 3 and 5 occur more than once.

The least common multiple is the product of all factors in the greatest number of their occurrence.

LCM = 3*3*3*3*5*5*13

LCM = 3^4 *5^2*13

LCM = 26,325

The least common multiple of 39, 81, 65 and 75 is 26,325.

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Answer 2

3l 39, 81, 65, 75

3| 13, 27, 65, 25

3l 13, 9, 65, 25

3| 13, 3, 65, 25

3l 13, 1, 65, 25

5l 13, 1, 13, 5

5l 13, 1, 13, 1

13l 1, 1, 1, 1

LCM:3×3×3×3×3×5×5×13= 78,975

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