What is the Least Common Multiple of 723 and 738?
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 738 is 177858.
LCM(723,738) = 177858
Least Common Multiple of 723 and 738 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 738, than apply into the LCM equation.
GCF(723,738) = 3
LCM(723,738) = ( 723 × 738) / 3
LCM(723,738) = 533574 / 3
LCM(723,738) = 177858
Least Common Multiple (LCM) of 723 and 738 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 723 and 738. First we will calculate the prime factors of 723 and 738.
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 738
Prime factors of 738 are 2, 3, 41. Prime factorization of 738 in exponential form is:
738 = 21 × 32 × 411
Now multiplying the highest exponent prime factors to calculate the LCM of 723 and 738.
LCM(723,738) = 32 × 2411 × 21 × 411
LCM(723,738) = 177858
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Related Least Common Multiples of 738
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