Important Questions For Class 10 Maths Chapter 1 | Q9

Real Numbers | LCM Word Problem

This CBSE class 10 Maths Extra Question IS from the chapter Real Numbers. This word problem tests your ability to understand that the given question is a word problem requiring the computation of LCM of 2 numbers.

Question - 9 : Anish goes fishing every 5th day and Balaji goes fishing every 7th day. If Anish and Balaji both went fishing today, how many days until they will go fishing on the same day again?


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Explanatory Answer | CBSE Extra Question | Real Numbers

Given: Anish goes fishing every 5th day.
Balaji goes fishing every 7th day.

Step 1 - Find the next instance when Anish and Balaji go fishing together

Let today be day 0.
Anish and Balaji went fishing today.
Anish will go fishing again in 5 days and again in another 5 days from then.
i.e., Anish will go fishing on the following days from today: 5, 10, 15, 20, ...
Anish will therefore, go fishing on days that are multiples of 5.

Balaji will go fishing again in 7 days and again in another 7 days from then.
i.e., Balaji will go fishing on the following days from today: 7, 14, 21, ....
Balaji will therefore, go fishing on days that are multiples of 7.

Anish and Balaji will go fishing on the same day again if that day is a multiple of 5 and 7.
i.e., on days that are common multiples of 5 and 7.
The first such common multiple is the lowest common multiple or LCM of 5 and 7.

Step 2 - Find LCM of 5 and 7

Step 1: Prime factorise 5 and 7
Both are prime numbers.

Step 2: LCM is the product of the largest power of all primes
= 5 × 7 = 35

They will go fishing on the same day again 35 days from today.

 

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