What is the Least Common Multiple of 1745 and 1755?

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 1745 and 1755 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1745 and 1755, than apply into the LCM equation.

GCF(1745,1755) = 5
LCM(1745,1755) = ( 1745 × 1755) / 5
LCM(1745,1755) = 3062475 / 5
LCM(1745,1755) = 612495

Least Common Multiple (LCM) of 1745 and 1755 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1745 and 1755. First we will calculate the prime factors of 1745 and 1755.

Prime Factorization of 1745

Prime Factorization of 1755

Now multiplying the highest exponent prime factors to calculate the LCM of 1745 and 1755.

LCM(1745,1755) = 5¹ × 349¹ × 3³ × 13¹
LCM(1745,1755) = 612495