Question

Find the L.C.M of 154 and 49.

Answer 1

LCM=1078

Explanation:

49=7×7

154=7×11×2

LCM=7×7×11×2

=1078

Answer 2

`\boxed{ \huge{ \bold{ \boxed{ \sf{1078}}}}}`

Explanation:

The L.C.M of any numbers can be obtained by using two methods and they are :

• Prime factorization method
• Division method

I am going to find the L.C.M of 154 and 49 by using these two methods :

1. Prime factorization method:

`\sf{154 \: and \: 49}`

First of all , find the prime factors of each numbers.

`\sf{154 =2 * 7 * 11}`

`\sf{49 \: = \: 7 * 7}`

Take out common prime factor i.e 7

Thenafter, also take out the other remaining prime factors : 2 , 11 and 7

L.C.M = Common factors × Remaining factors

= 7 × 2 × 11 × 7

= 1078

------------------------------------------------------------

Next method :

2. Division method

`\sf{154 \: and \: 49}`

Steps :

⇒ Arranging the given numbers in horizontal position.

⇒Thus, arranged numbers should be divided by a prime number. During this process that prime numbers should divide any two or more given numbers.

⇒Repeat the process till you get prime number as quotient for each number.

⇒The product of all prime factors and last quotients is L.C.M

( see attached picture )

Hope I helped!

Best regards!!