What is the Least Common Multiple of 1683 and 1692?

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 1683 and 1692 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1683 and 1692, than apply into the LCM equation.

GCF(1683,1692) = 9
LCM(1683,1692) = ( 1683 × 1692) / 9
LCM(1683,1692) = 2847636 / 9
LCM(1683,1692) = 316404

Least Common Multiple (LCM) of 1683 and 1692 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1683 and 1692. First we will calculate the prime factors of 1683 and 1692.

Prime Factorization of 1683

Prime Factorization of 1692

Now multiplying the highest exponent prime factors to calculate the LCM of 1683 and 1692.

LCM(1683,1692) = 3² × 11¹ × 17¹ × 2² × 47¹
LCM(1683,1692) = 316404