What is the Least Common Multiple of 723 and 732?
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 (LCM) of 723 and 732 is 176412.
LCM(723,732) = 176412
Least Common Multiple of 723 and 732 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 723 and 732, than apply into the LCM equation.
GCF(723,732) = 3
LCM(723,732) = ( 723 × 732) / 3
LCM(723,732) = 529236 / 3
LCM(723,732) = 176412
Least Common Multiple (LCM) of 723 and 732 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 723 and 732. First we will calculate the prime factors of 723 and 732.
Prime Factorization of 723
Prime factors of 723 are 3, 241. Prime factorization of 723 in exponential form is:
723 = 31 × 2411
Prime Factorization of 732
Prime factors of 732 are 2, 3, 61. Prime factorization of 732 in exponential form is:
732 = 22 × 31 × 611
Now multiplying the highest exponent prime factors to calculate the LCM of 723 and 732.
LCM(723,732) = 31 × 2411 × 22 × 611
LCM(723,732) = 176412
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