Question

What is the lcm of 48,56,72 using prime factorization method?

Answer 1

Prime factorization means  expressing a composite number in terms of prime numbers (product of prime numbers).

Prime factorization of 48

48 = 2*24 = 2*2*12 = 2*2*2*6 = 2*2*2*2*3

Hence, 48 can be written as: 2^4 * 3   ['^'-power.. 2^4*3 = 16*3=48]

Similarly, 56 = 7* 8 = 7*2^3

And, 72 = 9*8 = 3^2 * 2^3

So,

48 = 2^4 * 3

56 = 2^3 * 7

72 = 2^3 * 3^2

Now LCM is the product of 'highest powers' of all the prime factors of the given numbers.

Hence, LCM (48,56,72) = 2^4 * 3^2 * 7 = 16*9*7 = 1008

[Note that the highest power of '2' in the give numbers is 2^4 & highest power of '3' in given numbers is 3^2 && highest power of '7' is 7 itself]

Hence, LCM = 1008