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Question

(B) To find the smallest positive number divisible by every integer from $2$ to $10$,we need to calculate the Least Common Multiple $(LCM)$ of the num

Vedclass · Accepted Answer

$2520$

Vedclass · Answer

(B) To find the smallest positive number divisible by every integer from $2$ to $10$,we need to calculate the Least Common Multiple $(LCM)$ of the numbers $2, 3, 4, 5, 6, 7, 8, 9, 10$.First,write the prime factorization of each number:$2 = 2^1$$3 = 3^1$$4 = 2^2$$5 = 5^1$$6 = 2 	imes 3$$7 = 7^1$$8 = 2^3$$9 = 3^2$$10 = 2 	imes 5$The $LCM$ is found by taking the highest power of each prime factor present in the numbers:$LCM = 2^3 	imes 3^2 	imes 5^1 	imes 7^1$$LCM = 8 	imes 9 	imes 5 	imes 7$$LCM = 72 	imes 35 = 2520$.Therefore,the smallest positive number divisible by all integers from $2$ to $10$ is $2520$.

The smallest positive number divisible by every integer from $2$ to $10$ is:

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