What is the Least Common Multiple of 13749 and 13760?

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 13749 and 13760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13749 and 13760, than apply into the LCM equation.

GCF(13749,13760) = 1
LCM(13749,13760) = ( 13749 × 13760) / 1
LCM(13749,13760) = 189186240 / 1
LCM(13749,13760) = 189186240

Least Common Multiple (LCM) of 13749 and 13760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13749 and 13760. First we will calculate the prime factors of 13749 and 13760.

Prime Factorization of 13749

Prime Factorization of 13760

Now multiplying the highest exponent prime factors to calculate the LCM of 13749 and 13760.

LCM(13749,13760) = 3¹ × 4583¹ × 2⁶ × 5¹ × 43¹
LCM(13749,13760) = 189186240