Fundamental Theorem Of Arithmetic
(Prime Factorisation)
HCF
Product of the least powers of common prime factors of the numbers
LCM
Product of the highest powers of all the prime factors of the numbers
Every composite number can be expressed as a product of primes which is unique
Find HCF and LCM of 180 and 54
180
=
2
× 2
× 3
× 3
=
22
× 32
54
=
2
× 3
× 3
× 3
=
2
× 33
HCF
× 5
× 5
= 2
× 32
= 2 × 9
= 18
LCM
= 22
× 33
= 4 × 27 × 5
= 540
× 5
HCF × LCM
= 18 × 540
= 9720
PRODUCT OF NUMBERS
= 54 × 180
= 9720
HCF(a, b) × LCM (a, b) = a × b