Question

LCM of 112,144 and 180​

Answer 1

Required Answer :

Kindly refer the attachment for your answer!

Least Common Multiple ( LCM ) :

The smallest number that can divide two or more given numbers without leaving any remainder is called the lowest common multiple. Lowest common multiple is also called the least common multiple and is written as LCM. Always remember that, whenever words like 'least' 'smallest' 'lowest' are used we have to take out thae LCM.

Highest Comment Multiple ( HCF ) :

The greatest number that can divide two or more given numbers without leaving any remainder is called the highest common multiple. Highest common multiple is written as HCF. Always remember that, whenever words like 'greatest' 'highest' 'largest' are used we have to take out the HCF.

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Answer 2

• The least common multiple of two or more natural numbers is the least natural number that is a multiple of given numbers.
• The Lowest Common Multiple (LCM) of 112, 114 and 180 is 5040.

Step-by-step explanation:

$\underline{\bf{\red{Synthetic\: division\: method:}}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\begin{gathered} \begin{array}{c|c} \underline{\sf{2}}& \underline{\sf{112 \: \: \: \: \: 144 \: \: \: \: \: 180}} \\ \underline{\sf{2}}&\underline{\sf{ \: 56 \: \: \: \: \: \: \: \: 72 \: \: \: \: \: \: \: 90 \: }} \\\underline{\sf{2}}&\underline{\sf{\: 28 \: \: \: \: \: \: \: \: 36 \: \: \: \: \: \: \: 45 \:}} \\\underline{\sf{2}}&\underline{\sf{ \: 14 \: \: \: \: \: \: \: \: 18 \: \: \: \: \: \: \: 45 \: }} \\\underline{\sf{7}}&\underline{\sf{ \: 7 \: \: \: \: \: \: \: \: \: \: 9 \: \: \: \: \: \: \: \: \: 45 \:}} \\\underline{\sf{3}}&\underline{\sf{\: 1 \: \: \: \: \: \: \: \: \: \: 9\: \: \: \: \: \: \: \: \: 45 \: }}\\\underline{\sf{3}}&\underline{\sf{\: 1 \: \: \: \: \: \: \: \: \: \: 3\: \: \: \: \: \: \: \: \: 15 \: }}\\\underline{\sf{5}}&\underline{\sf{\: 1 \: \: \: \: \: \: \: \: \: \: 1\: \: \: \: \: \: \: \: \: \: \: 5 \: }}\\&\sf{\: 1 \: \: \: \: \: \: \: \: \: \: 1\: \: \: \: \: \: \: \: \: \: \: 1 \: } \\ \end{array}\end{gathered}$

$\\ \longmapsto{\sf{LCM= \underline{2 \times 2 }\times \underline{ 2 \times 2} \times \underline{7 \times 3 }\times \underline{3 \times 5}}}$

$\\ \longmapsto{ \sf{ LCM=\underline{4 \times 4} \times \underline{21 \times 15}}}$

$\\ \longmapsto{ \sf{LCM=\underline{16\times 315}}}$

$\\ \longmapsto{\boxed{\boxed{\sf{LCM= \frak{\red{5040}}}}}}$

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Additional Information:-

↪What is meant by relatively prime numer?

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎To reduce a fraction to its lowest term, it's numerator and denominator are divided by their HCF; for example, $\sf{\dfrac{42}{60}=\dfrac{42\div 6}{60\div 6}=\dfrac{7}{10}}$.

When numerator and denominator do not have a common factor other than 1, they are called relatively prime. In other words, the two numbers having 1 as their HCF are called relatively prime numbers.

Some pairs of relatively prime numbers are 20 and 33, 12 and 13, 77 and 791.

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