# What is the LCM of 144, 180, and 192?

LCM of 144, 180 and 192 is the smallest number that is exactly divisible by all of them.

## Answer: LCM of 144, 180 and 192 is 2880

The least common multiple of 144, 180 and 192 is the smallest number that is exactly divisible by three of them without any remainder.

## Explanation:

### LCM of 144, 180 and 192 by Prime factorization:

In this method, we first write 144, 180 and 192 as the product of their prime factors and then multiply the common and uncommon factors to get the LCM.

Prime factorization of 144= 2×2×2×2×3×3 = 2^{4} x 3^{2}

Prime factorization of 180= 2×2×3×3×5 = 2^{2} x 3^{2} x 5, and

Prime factorization of 192 = 2×2×2×2×2×2×3 = 2^{6} x 3

In the prime factorization of 144, 180 and 192 the prime factor 2 occurs 6 times, prime factor 3 occurs 2 times and prime factor 5 occurs once.

So, the product of all these is 2^{6 }×3^{2 }×5 = 64×9×5 = 2880.

Therefore LCM144, 180,192) = 2880

### LCM of 144, 180 and 192 by Division Method:

In this division method, we divide 144, 180 and 192 simultaneously with prime numbers and stop it when we don't have a prime number to divide them further. Product of the prime numbers used is the LCM of 144 180 and 192.