The least number that is divisible by all the | vedclass

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(C) To find the least number divisible by all numbers from $1$ to $10$,we need to calculate the Least Common Multiple $(LCM)$ of these numbers.Prime f

Vedclass · Accepted Answer

$2520$

Vedclass · Answer

(C) To find the least number divisible by all numbers from $1$ to $10$,we need to calculate the Least Common Multiple $(LCM)$ of these numbers.Prime factorization of each number from $1$ to $10$:$1 = 1$$2 = 2^1$$3 = 3^1$$4 = 2^2$$5 = 5^1$$6 = 2^1 	imes 3^1$$7 = 7^1$$8 = 2^3$$9 = 3^2$$10 = 2^1 	imes 5^1$The $LCM$ is found by taking the highest power of each prime factor present in the numbers:$LCM = 2^3 	imes 3^2 	imes 5^1 	imes 7^1$$LCM = 8 	imes 9 	imes 5 	imes 7$$LCM = 72 	imes 35 = 2520$Thus,the least number divisible by all numbers from $1$ to $10$ is $2520$.

The least number that is divisible by all the numbers from $1$ to $10$ (both inclusive) is

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