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# What is the least multiple of 9 which leaves a remainder of 3 when divided by each 4, 6 and 7?a) 171b) 74c) 99d) 364 Correct answer is option 'A'. Can you explain this answer?

## CAT Question

By Vikas Upadhyay · Oct 06, 2018 ·CAT
Priya Tiwari answered 2 weeks ago
First we take LCM of 4,6,7 is 84 so, no. will be
84x+3, which is multiple of 9.
now go through the option.
option a is multiple of 9 and if we divide with 84 it gives remainder as 3.
so option ' a ' is correct.

Nayana Kowshik answered Mar 23, 2020
Yes it is op A 171..divide 171 by 4,6, and 7.when divided by each the remainder is 3...so..

Vibhor E L U answered Jun 24, 2019
For least multiple, divisor must be equal to dividend such that the quotient = 1.
(9k - 3)/(4×6×7) = 1
9k = 168 + 3 = 171.

Hariharan See answered Aug 12, 2018
A

Lcm of 4,6,7=168Answer is 168+3=171Where 3 is remainder

Prerna Shankar answered Oct 06, 2018
L.C.M. of 6, 9, 15 and 18 is 90.
Let required number be 90k + 4, which is multiple of 7.
Least value of k for which (90k + 4) is divisible by 7 is k = 4.
∴Required number = (90 x 4) + 4 = 364.

Krati Mangal answered May 27, 2020
Yes..when remainder is same then the first such number will be LCM(divisiors) + remainder...so the first number will be 84.but 84 is not divisible by 9 so add the LCM again to get next number , which is 171.