What is the Least Common Multiple of 690 and 705?

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 690 and 705 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 690 and 705, than apply into the LCM equation.

GCF(690,705) = 15
LCM(690,705) = ( 690 × 705) / 15
LCM(690,705) = 486450 / 15
LCM(690,705) = 32430

Least Common Multiple (LCM) of 690 and 705 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 690 and 705. First we will calculate the prime factors of 690 and 705.

Prime Factorization of 690

Prime Factorization of 705

Now multiplying the highest exponent prime factors to calculate the LCM of 690 and 705.

LCM(690,705) = 2¹ × 3¹ × 5¹ × 23¹ × 47¹
LCM(690,705) = 32430