5. Find the smallest number which leaves the remainder 8 and 12 when divided by 28 and 32 respectively.
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5. Find the smallest number which leaves the remainder 8 and 12 when divided by 28 and 32 respectively.
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Solution:First, find the LCM of 28 and 32 which is 224.
Using the remainder rule:
dividend = divisor*quotient + remainder
224 = 28 * 8 - No remainder.
But
224 = 216 + 8 -Because you want R = 8
224 = 28 * 7 = (196 + 20) + 8
224 - 20 = 28 * 7 + 8 .... 1
Similarly
224 = 32 * 7 = 0
But
224 = 212 + 12 -Because you want R = 12
224 = 32 * 6 = (192 + 20) + 12
224 - 20 = 32 * 6 + 12 .... 2
Therefore, the smallest dividend = 224 - 20 = 204
To check:
204 divided by 28, remainder = 8
204 divided by 32, remainder = 12
Hope this will help.