What is the Least Common Multiple of 728 and 745?
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 728 and 745 is 542360.
LCM(728,745) = 542360
Least Common Multiple of 728 and 745 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 728 and 745, than apply into the LCM equation.
GCF(728,745) = 1
LCM(728,745) = ( 728 × 745) / 1
LCM(728,745) = 542360 / 1
LCM(728,745) = 542360
Least Common Multiple (LCM) of 728 and 745 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 728 and 745. First we will calculate the prime factors of 728 and 745.
Prime Factorization of 728
Prime factors of 728 are 2, 7, 13. Prime factorization of 728 in exponential form is:
728 = 23 × 71 × 131
Prime Factorization of 745
Prime factors of 745 are 5, 149. Prime factorization of 745 in exponential form is:
745 = 51 × 1491
Now multiplying the highest exponent prime factors to calculate the LCM of 728 and 745.
LCM(728,745) = 23 × 71 × 131 × 51 × 1491
LCM(728,745) = 542360
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