What is the Least Common Multiple of 49680 and 49688?

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 49680 and 49688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49680 and 49688, than apply into the LCM equation.

GCF(49680,49688) = 8
LCM(49680,49688) = ( 49680 × 49688) / 8
LCM(49680,49688) = 2468499840 / 8
LCM(49680,49688) = 308562480

Least Common Multiple (LCM) of 49680 and 49688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49680 and 49688. First we will calculate the prime factors of 49680 and 49688.

Prime Factorization of 49680

Prime Factorization of 49688

Now multiplying the highest exponent prime factors to calculate the LCM of 49680 and 49688.

LCM(49680,49688) = 2⁴ × 3³ × 5¹ × 23¹ × 6211¹
LCM(49680,49688) = 308562480