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Find LCM of 105 and 120 and hence find HCF

Answer»

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} <klux>3</klux> & 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.


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