What is the Least Common Multiple of 1740 and 1760?

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 1740 and 1760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1740 and 1760, than apply into the LCM equation.

GCF(1740,1760) = 20
LCM(1740,1760) = ( 1740 × 1760) / 20
LCM(1740,1760) = 3062400 / 20
LCM(1740,1760) = 153120

Least Common Multiple (LCM) of 1740 and 1760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1740 and 1760. First we will calculate the prime factors of 1740 and 1760.

Prime Factorization of 1740

Prime Factorization of 1760

Now multiplying the highest exponent prime factors to calculate the LCM of 1740 and 1760.

LCM(1740,1760) = 2⁵ × 3¹ × 5¹ × 29¹ × 11¹
LCM(1740,1760) = 153120