Question

ind the least number that is divisible by all the numbers between 6 and 12.
ind the least number of six digits which is divisible by each of 10, 12, 15 and I​

Answer 1

Answer:

5

Step-by-step explanation:

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Let the least number of six digits, which when divided by 4, 6, 10 and 15, leaves in each case the same remainder of 2, be N . The sum of the digits in N is ?

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Hint: Find the least number of six digits which when divided by 4, 6, 10 and 15 leaves 2 as a remainder . Use LCM of 4, 6, 10 and 15 to find that number and divide the least six digit number with that LCM. You’ll get a remainder and quotient. Now, subtract remainder from LCM (divisor) and add the least six digit number taken. You’ll get a number which satisfies the condition of the question. Then, add all terms of that number and you’ll get the final answer.

Complete step-by-step answer:

Least six digit number = 100000

Let us find the smallest number divisible by 4 , 6 , 10 , 15

i.e LCM of 4 , 6 , 10 , 15 = 60 ( using prime factorization method )

Let us divide 100000 by 60 to check the remainder and find the smallest six digit number divisible by 60.

⇒10000060 remainder = 40 , quotient = 1666

Now to find the number divisible by 60 we need to subtract 40 from 100000 but if we do that it becomes a five digit number . Therefore the next divisible number would be 100000+(60−40)=100020

Which leaves the remainder 0 , but the least number of six digits (N) , which when divided by 4, 6, 10 and 15, leaves in each case the same remainder of 2 will be 100020+2 = 100022

Therefore the sum of digits = 1+0+0+0+2+2= 5