Question

find LCM of 105 and 120 and hence find HCF

Answer 1

Correct Question :

Find L.C.M and H.C.F of ( 120 , 105 ).

AnsWer :

H.C.F = 15. and L.C.M 840.

Given :

• N1 = 120.
• N2 = 105.

Solution :

Prime factor of 120.

$\begin{array}{r | l} 2 & 120 \\ \cline{2-2} 2 & 60 \\ \cline{2-2} 3 & 30 \\ \cline{2-2} 5 & 10 \\ \cline{2-2} 2 & 2 \\ \cline{2-2} & 1 \end{array}$

Prime factor of 105.

$\begin{array}{r | l}5 & 105 \\ \cline{2-2} 3 & 21 \\ \cline{2-2} 7 & 7 \\ \cline{2-2} & 1 \end{array}$

Now,

Product

$\bigstar \tt \: 120 \dashrightarrow2 \times 2 \times 2 \times 3 \times 5.$

$\bigstar \tt \: 105 \dashrightarrow5 \times 3 \times 7.$

For, HCF => 5*3 = 15.

For, LCM => 5*3*8*7 = 840.

Therefore, the value of HCF is 15 and LCM is 840.

Some information :

H.C.F - Highest Common factor.

L.C.M - Least common multiple.

Answer 2

Answer:-

HCF × LCM = 105 × 120 .

Explanation:-

The given numbers are 105 and 120.

The factors of given numbers are

105 = 3 × 5 × 7

120 = 2 × 2 × 2 × 3 × 5

5LCM of 105 and 120 is,

LCM = 3 × 5 = 15

HCF of 105 and 120 is,

HCF = 2 × 2 × 2b× 3 × 5 × 7 = 840

Product of 105 and 120 is

105 × 120 = 12600

Product of LCM and HCF of 105 and 120.

15 × 840 = 21600

Hence proved that HCF × LCM = 105 × 120