What is the Least Common Multiple of 49 and 144?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 49 and 144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49 and 144, than apply into the LCM equation.

GCF(49,144) = 1
LCM(49,144) = ( 49 × 144) / 1
LCM(49,144) = 7056 / 1
LCM(49,144) = 7056

Least Common Multiple (LCM) of 49 and 144 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49 and 144. First we will calculate the prime factors of 49 and 144.

Prime Factorization of 49

Prime Factorization of 144

Now multiplying the highest exponent prime factors to calculate the LCM of 49 and 144.

LCM(49,144) = 7² × 2⁴ × 3²
LCM(49,144) = 7056