1/3/2023 0 Comments Least i number![]() ![]() ![]() Note: We will prove that if a is the smallest number which on division by 21, 33 and 45 leaves remainder 0, then a-3 is the smallest number which on division by 24, 36 and 45 leaves remainder 21, 33 and 45. Hence the smallest number which divides by 24,36 and 48 leaves remains 21, 33 and 45 respectively is a-3 = 144-3 = 141. Hence from the definition of L, we have 24|L, 36|L and 48|L ![]() Since 21 =24-3, 33 = 36 – 3 and 45 = 48 -3, if a is the smallest number which on division by 21, 33 and 45 leaves remainder 0, then a-3 is the smallest number which on division by 24, 36 and 45 leaves remainder 21, 33 and 45. Hint: Observe that 21 =24-3, 33 = 36 – 3 and 45 = 48 -3.Hence if a be the smallest number which on division by 21, 33 and 45 leaves remainder 0, then a-3 is the smallest number which on division by 24, 36 and 45 leaves remainder 21, 33 and 45. ![]()
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