What is the Least Common Multiple of 415 and 430?
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 415 and 430 is 35690.
LCM(415,430) = 35690
Least Common Multiple of 415 and 430 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 415 and 430, than apply into the LCM equation.
GCF(415,430) = 5
LCM(415,430) = ( 415 × 430) / 5
LCM(415,430) = 178450 / 5
LCM(415,430) = 35690
Least Common Multiple (LCM) of 415 and 430 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 415 and 430. First we will calculate the prime factors of 415 and 430.
Prime Factorization of 415
Prime factors of 415 are 5, 83. Prime factorization of 415 in exponential form is:
415 = 51 × 831
Prime Factorization of 430
Prime factors of 430 are 2, 5, 43. Prime factorization of 430 in exponential form is:
430 = 21 × 51 × 431
Now multiplying the highest exponent prime factors to calculate the LCM of 415 and 430.
LCM(415,430) = 51 × 831 × 21 × 431
LCM(415,430) = 35690
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