What is the Least Common Multiple of 1650 and 1670?

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 1650 and 1670 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1650 and 1670, than apply into the LCM equation.

GCF(1650,1670) = 10
LCM(1650,1670) = ( 1650 × 1670) / 10
LCM(1650,1670) = 2755500 / 10
LCM(1650,1670) = 275550

Least Common Multiple (LCM) of 1650 and 1670 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1650 and 1670. First we will calculate the prime factors of 1650 and 1670.

Prime Factorization of 1650

Prime Factorization of 1670

Now multiplying the highest exponent prime factors to calculate the LCM of 1650 and 1670.

LCM(1650,1670) = 2¹ × 3¹ × 5² × 11¹ × 167¹
LCM(1650,1670) = 275550