Question

HCF and LCM of 135 120 and 180

Answer 1

Step-by-step explanation:

LCM of 120 and 135 is 1080.

HCF of 135 120 and 180 is 15

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Answer 2

HCF = 15

LCM = 1080

Explanation

How to calculate HCF?

HCF 135,120 and 180

Solution:

Step 1: List all of the factors of the given numbers.

Factors of 135:  1, 3, 5, 9, 15, 27, 45 and 135.

Factors of 120:  1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120

Factors of 180:  1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180.

Step 2: Circle or highlight the numbers that exist in the factors of both numbers and should be the greatest common number. In this case, 3 is the largest common number in both of them.

Factors of 135: 1, 3, 5, 15.

Factors of 120: 1, 3, 5, 15

Factors of 180: 1, 3, 5, 15

So, HCF = 15.

How to calculate LCM?

Find LCM of 135, 120, and 180 using prime factorization?

Solution:

Step 1: List the prime factors of the given numbers.

135: 5 x 3 x 3 x 3 = 5 x 3³

120: 5 x 3 x 2 x 2 x 2 = 5 x 3 x 2³

180: 5 x 3 x 3 x 2 x 2 = 5 x 3² x 2 ²

Step 2: To get the LCM, multiply the prime factors. Use the common factors only once when multiplying.

135 =  5 x 3³

120 = 5 x 3 x 2³

180 = 5 x 3² x 2²

5 x 3³ x 2³=  1080

So, LCM (135, 120, 180) = 1080

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