What is the Least Common Multiple of 1785 and 1792?

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 1785 and 1792 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1785 and 1792, than apply into the LCM equation.

GCF(1785,1792) = 7
LCM(1785,1792) = ( 1785 × 1792) / 7
LCM(1785,1792) = 3198720 / 7
LCM(1785,1792) = 456960

Least Common Multiple (LCM) of 1785 and 1792 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1785 and 1792. First we will calculate the prime factors of 1785 and 1792.

Prime Factorization of 1785

Prime Factorization of 1792

Now multiplying the highest exponent prime factors to calculate the LCM of 1785 and 1792.

LCM(1785,1792) = 3¹ × 5¹ × 7¹ × 17¹ × 2⁸
LCM(1785,1792) = 456960