What is the Least Common Multiple of 13725 and 13745?
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 13725 and 13745 is 37730025.
LCM(13725,13745) = 37730025
Least Common Multiple of 13725 and 13745 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13725 and 13745, than apply into the LCM equation.
GCF(13725,13745) = 5
LCM(13725,13745) = ( 13725 × 13745) / 5
LCM(13725,13745) = 188650125 / 5
LCM(13725,13745) = 37730025
Least Common Multiple (LCM) of 13725 and 13745 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 13725 and 13745. First we will calculate the prime factors of 13725 and 13745.
Prime Factorization of 13725
Prime factors of 13725 are 3, 5, 61. Prime factorization of 13725 in exponential form is:
13725 = 32 × 52 × 611
Prime Factorization of 13745
Prime factors of 13745 are 5, 2749. Prime factorization of 13745 in exponential form is:
13745 = 51 × 27491
Now multiplying the highest exponent prime factors to calculate the LCM of 13725 and 13745.
LCM(13725,13745) = 32 × 52 × 611 × 27491
LCM(13725,13745) = 37730025
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