This question is taken from real numbers chapter in which we have given three numbers 35, 56 and 91 and we have been asked to find the smallest number which when divided by the above number leaves remainder 7 in each case.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 1B, question no 10

The smallest number which when divided byÂ 35,56Â andÂ 91=Â LCM ofÂ 35,56Â andÂ 91

35=5Ã—7

56=2Ã—2Ã—2Ã—7

91=7Ã—13

LCMÂ =7Ã—5Ã—2Ã—2Ã—2Ã—13=3640

The smallest number that when divided byÂ 35,56,91Â leaves a remainderÂ 7Â in each caseÂ =3640+7=3647.