# How to Find the HCF and LCM of 90 and 144 By Using Prime Factorization Method?

HCF (Highest Common Factor) of 90 and 144 is the largest possible number which divides both 90 and 144 exactly.

Least Common Multiple of 90 and 144 is the smallest number which is exactly divisible by 90 and 144.

## Answer: HCF of 90 and 144 is 18, and the LCM of 90 and 144 is 720

We will explain the prime factorization method to find the HCF and the LCM of 90, 144.

**Explanation:**

### HCF of 90 and 144 by Listing the Common Factors

Let us list the factors and identify the common factors. the biggest number among them is the HCF.

Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

Common Factors of 90 and 144: 1, 2, 3, 6, 9, 18

Since the greatest common factor of 90 and 144 is 18, HCF of 90 and 144 is 18

### LCM of 90 and 144 by Formula

The formula of LCM is LCM (a, b) = (a × b) / HCF (a, b)

HCF (90,144) = 18

Therefore, LCM of 90 and 144 = (90 × 144) / 18

= 12960 / 18

= 720

So, LCM of 90 and 144 = 720

### Therefore, the HCF is 18, and LCM is 720.

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