What is the Least Common Multiple of 729 and 749?
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 729 and 749 is 546021.
LCM(729,749) = 546021
Least Common Multiple of 729 and 749 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 729 and 749, than apply into the LCM equation.
GCF(729,749) = 1
LCM(729,749) = ( 729 × 749) / 1
LCM(729,749) = 546021 / 1
LCM(729,749) = 546021
Least Common Multiple (LCM) of 729 and 749 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 729 and 749. First we will calculate the prime factors of 729 and 749.
Prime Factorization of 729
Prime factors of 729 are 3. Prime factorization of 729 in exponential form is:
729 = 36
Prime Factorization of 749
Prime factors of 749 are 7, 107. Prime factorization of 749 in exponential form is:
749 = 71 × 1071
Now multiplying the highest exponent prime factors to calculate the LCM of 729 and 749.
LCM(729,749) = 36 × 71 × 1071
LCM(729,749) = 546021
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