Question

find lcm and hcf of 180 and 92 and verify​

Answer 1

Answer:

Step-by-step explanation:

Hcf of 180 & 92 is 4 and Lcm is 8740

Answer 2

Answer :-

LCM = 4140

HCF = 4

Explanation :-

$\textsf{\underline{\underline{LCM of 180 and 92 :}}}$

$\begin{array}{r|l} 2 & 180,92 \\\cline{1-2} 2 & 90,46 \\\cline{1-2} 5 & 45,23 \\ \cline{1-2} 3 & 9,23 \\\cline{1-2} 3 & 3,23 \\\cline{1-2} 23 & 1,23 \\\cline{1-2} & 1,1 \end{array}$

LCM = 2 × 2 × 5 × 3 × 3 × 23 = 4140

$\boxed{\boxed{\sf{LCM = 4140}}}$

$\textsf{\underline{\underline{HCF of 180 and 92 }}}$

$\textsf{Prime Factorization of 180 :}$

$\begin{array}{r|l} 2 & 180 \\\cline{1-2} 2 & 90 \\\cline{1-2} 5 & 45 \\ \cline{1-2} 3 & 9 \\\cline{1-2} 3 & 3 \\\cline{1-2} & 1 \end{array}$

$\textsf{Prime Factorization of 92}$

$\begin{array}{r|l} 2 & 92 \\\cline{1-2} 2 & 46 \\\cline{1-2} 23 & 23 \\ \cline{1-2} & 1 \end{array}$

$\sf{\implies} \: 180 = \underline{\red{2 \times 2}} \times 5 \times 3 \times 3$

$\sf{\implies} \: 92 = \underline{\red{2 \times 2}}\times 23$

HCF = 2 × 2 = 4

$\boxed{\boxed{\sf{HCF = 4}}}$

$\textsf{LCM = 4140}$

$\textsf{HCF = 4}$

Verification of the Relation between HCF and LCM.

$\boxed{\sf{HCF \times LCM = Product\:of\:2\:numbers}}$

Two numbers = 4140 and 4

LCM = 4140

HCF = 4

$\sf{\implies} \: 180 \times 92 = 4140 \times 4$

$\sf{\implies} \: 16560 = 16560$

Both sides are equal.

Hence, Verified !