Question

Find the lcm and hcf of 840 and 144 by applying the fundamental theorem of arithmetic.

Answer 1

Solution :-

Fundamental Theorem of Arithmetic -

The Fundamental Theorem of Arithmetic says that every composite number can be factorized as a product of prime numbers and this factorization is unique, apart from the order in which the prime factors occur. 

840 = 2*2*2*3*5*7

144 = 2*2*2*2*3*3

L.C.M. of 840 and 144 = 2*2*2*2*3*3*5*7 

= 5040

H.C.F. of 840 and 144 = 2*2*2*3

= 24

Answer.

Answer 2

To find the LCM and HCF of 840 and 144 using "fundamental theorem of arithmetic".

Solution:

Fundamental Theorem of Arithmetic says that,

1. Factorize given composite number into product of prime numbers

$840=2 \times 2 \times 2 \times 3 \times 5 \times 7$

$144=2 \times 2 \times 2 \times 2 \times 3 \times 3$

2. The factorized numbers should be unique.

3. Find the LCM and HCF of the given numbers using factorization.

First take the LCM of the both number commonly.

L.C.M. of 840 and $144 =2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 7$

L.C.M. of 840 and 144 = 5040

Take the HCF, we need to factorize separately then find the common factor obtained by the factorization, we need get the common numbers from the factorization. On multiplying the common numbers, we get highest common factor.

H.C.F. of 840 and $144 =2 \times 2 \times 2 \times 3$

H.C.F. of 840 and 144 = 24