Let n be an integer greater than 100 such that the L.C.M. of 1, 2, 3, … n is equal to the L.C.M. of 101, 102 ,…, n. Find the product of all digits of the smallest possible value of n.
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Given : n be an integer greater than 100 such that the L.C.M. of 1, 2, 3, … n is equal to the L.C.M. of 101, 102 ,…, n.
To find : the product of all digits of the smallest possible value of n.
Solution:
L.C.M. of 1, 2, 3, … n is equal to the L.C.M. of 101, 102 ,…, n.
Let find prime number less than 101
that is 97
So LCM of 101, 102 ,…, n. must have a number having a number multiple of 97
97 * 2 = 194
hence n should be atleast 194
product of all digits of the smallest possible value of n
= 1 * 9 * 4
= 36
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