What is the Least Common Multiple of 61680 and 61698?

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 61680 and 61698 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 61680 and 61698, than apply into the LCM equation.

GCF(61680,61698) = 6
LCM(61680,61698) = ( 61680 × 61698) / 6
LCM(61680,61698) = 3805532640 / 6
LCM(61680,61698) = 634255440

Least Common Multiple (LCM) of 61680 and 61698 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 61680 and 61698. First we will calculate the prime factors of 61680 and 61698.

Prime Factorization of 61680

Prime Factorization of 61698

Now multiplying the highest exponent prime factors to calculate the LCM of 61680 and 61698.

LCM(61680,61698) = 2⁴ × 3¹ × 5¹ × 257¹ × 7¹ × 13¹ × 113¹
LCM(61680,61698) = 634255440