Find the lowest natural number which when divided by 10 50 15 leaves the remainder of 5 in each case

Solution:

We will be using the concept of LCM(Least Common Multiple) to solve this.

To determine the least number which when divided by 6, 15, and 18 leave the remainder 5 in each case,we need to find the LCM of the three given numbers.

Since, the LCM obtained will be the smallest common multiple of all the three numbers 6, 15, and 18, after getting LCM we need to add 5  to it so as to get 5 as a remainder.

Let's find the LCM of 6, 5 and 18 as shown below.

Therefore, LCM of 6, 15 and 18 = 2 × 3 × 3 × 5 = 90.

Thus we can see that, 90 is the least number exactly divisible by 6, 15, and 18.

To get a remainder 5, we need to add 5 to the LCM.

⇒ 90 + 5 = 95.

Thus, when 95 is divided by 6, 15, and 18 we get a remainder of 5 in each case.

Hence, the required number for the given problem is 95.

You can also use the LCM Calculator to solve this.

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NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 Question 8

Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case

Summary:

The least number which when divided by 6, 15, and 18 leaving a remainder of 5 in each case will be 95.

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LCM is the smallest positive number that is a multiple of two or more numbers.

Answer: 95 is the least number which when divided by 6, 15, and 18 leaves a remainder of 5 in each case.

To find the least number which when divided by 6, 15, and 18 leaves a remainder of 5 in each case we have to do the following steps:

• Find the LCM of 6, 15 and 18
• Add 5 to the LCM 

Explanation:

Below is the LCM shown for 6,15 and 18 using prime factorization.

6 = 2 × 3

15 = 3 × 5

18 = 2 × 3 × 3

Thus, the LCM of 6,15 and 18 = 2 × 3 × 3 × 5 = 90

Now, adding 5 to 90, we get 90 + 5 = 95

Verification:

1) 95/6
Quotient = 15
Remainder = 5

2) 95/15
Quotient = 6
Remainder = 5

3) 95/18
Quotient = 5
Remainder = 5

Hence, 95 is the least number which when divided by 6, 15, and 18 leaves a remainder of 5 in each case.

Find the least number which when divided by 6, 15 and 18, leave remainder 5 in each case.

Solution

Find the LCM of given numbersGiven numbers: 6,15,18 can be written in prime factors as6=2×315=3×5and18=2×3×3∴LCM6,15,18=2×3×3×5=90.The number that is 5 more than the LCM of the given numbers will leave a remainder of 5 when divided by these numbers.So, the required number is 90+5=95. (adsbygoogle = window.adsbygoogle || []).push({}); Therefore, when 95 is divided by the given numbers, it will leave a remainder of 5.

Find the least number which when divided by 15, leaves a remainder of 5, when divided by 25, leaves a remainder of 15 and when divided by 35 leaves a remainder of 25.A.515B.525C.1040D.1050

Answer

Verified

Hint: Here we will use the concept of the LCM. Firstly we will find the LCM of all the divisors i.e. 15, 25 and 35. Then we will see the pattern of getting the remainder by observing the difference between the divisor and the remainder. Then we will subtract the observed difference from the LCM of all the divisors to get the required value.Complete step-by-step answer:
First, we will find the LCM of the divisors of the number i.e. 15, 25 and 35. Therefore, we get

LCM of 15, 25 and 35 \[ = 3 \times 5 \times 5 \times 7 = 525\]
LCM of 15, 25 and 35 is equal to 525.
We know that when the divisor is 15 the remainder is 5, when the divisor is 25 the remainder is 15 and when the divisor is 35 the remainder of 25.
Now we can see that when the number is divided by the divisors then the remainder obtained is always 10 less than the divisor.
So, this means that the required number must be 10 less than the LCM of the divisors. Therefore, we get
Required number \[ = 525 - 10 = 515\]
Hence, the least number which satisfies the given condition is equal to 515.
So, option A is the correct option.

Note: Remainder is the value of the left over when a number is not exactly divisible by the other number. Zero is the remainder when a number exactly divides the other number.
In addition, we should know how to find the LCM (Least Common Multiple) of the numbers. LCM is the smallest positive integer that is divisible by the numbers. Here we should note that HCF is the short form of highest common factor which is the largest factor which is the largest common divisor of both the numbers.

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