Question

State fundamental theorem of arithmetic. Find the LCM and HCF of 312
and 27 and verify LCM * HCF= product of the numbers.

Answer 1

Fundamental theorem of arithmetic is stated as “ every composite number can be expressed as a product of primes and this factorization is unique except for the order in which the prime factors occur”
Factors of 312 = 2*2*2*3*13
Factors of 27 = 3*3*3
Lcm = 2*2*2*2*3*3*3*13=2808
Hcf = 3
Lcm* hcf = 2808 *3 = 8424
312*27 =8424
Thus verified