Problems on H.C.F and L.C.M - Arithmetic Aptitude Questions and Answers

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What is the least multiple of 7 which when divided by 6, 9, 15, and 18 respectively, leaves 4 as the remainder in each case?

364

255

385

266

Answer : Option A

Explanation :

Take LCM of 6, 9, 15, and 18. Their LCM = 90
As per given information, (90* x+4)/7

(90 *x)/ 7 = ((7 * 12 *x) + 6x + 4)/7
Or, (7*12x)/7 + (6x + 4)/7

x=4 satisfy the condition.
Hence, the required number is 90 * 4 + 4 = 364.

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