What is the Least Common Multiple of 17754 and 17760?

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 17754 and 17760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17754 and 17760, than apply into the LCM equation.

GCF(17754,17760) = 6
LCM(17754,17760) = ( 17754 × 17760) / 6
LCM(17754,17760) = 315311040 / 6
LCM(17754,17760) = 52551840

Least Common Multiple (LCM) of 17754 and 17760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17754 and 17760. First we will calculate the prime factors of 17754 and 17760.

Prime Factorization of 17754

Prime Factorization of 17760

Now multiplying the highest exponent prime factors to calculate the LCM of 17754 and 17760.

LCM(17754,17760) = 2⁵ × 3¹ × 11¹ × 269¹ × 5¹ × 37¹
LCM(17754,17760) = 52551840