What is the Least Common Multiple of 689 and 708?

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 689 and 708 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 689 and 708, than apply into the LCM equation.

GCF(689,708) = 1
LCM(689,708) = ( 689 × 708) / 1
LCM(689,708) = 487812 / 1
LCM(689,708) = 487812

Least Common Multiple (LCM) of 689 and 708 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 689 and 708. First we will calculate the prime factors of 689 and 708.

Prime Factorization of 689

Prime Factorization of 708

Now multiplying the highest exponent prime factors to calculate the LCM of 689 and 708.

LCM(689,708) = 13¹ × 53¹ × 2² × 3¹ × 59¹
LCM(689,708) = 487812