Question

Find the smallest number divisible by numbers 2 to 9 (both inclusive}

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The given question is Find the smallest number divisible by numbers 2 to 9 (both inclusive}

The solution to this question is we have to find the smallest number that is divisible by the numbers from 2 to 9. where 2 and 9 are both included.

we have to find the LCM of the numbers.

The lcm of these numbers can be obtained by the prime factorisation method.

The prime factorisation method is used to calculate both HCF and the LCM

The LCM of the numbers from 2 to 9 is

$2)2 \: 3 \: 4 \: 5 \: 6 \: 7 \: 8 \: 9 \\2 )1 \: 3 \: 2 \: 5 \: 3\: 7 \: 4 \: 9 \\ 3)1 \: 3 \: 1 \: 5 \: 3 \: 7 \: 2 \: 9 \\ 3)1 \: 1 \: 1 \: 5 \: 1 \: 7 \: 2 \: 3\\ 2)1 \: 1 \: 1 \: 5 \: 1 \: 7 \: 1 \: 1\\ 5)1 \: 1 \: 1 \: 1 \: 1 \: 7 \: 1 \: 1\\ 7)1 \: 1 \: 1 \: 1 \: 1 \: 1 \: 1 \: 1$

Therefore, the LCM of the given numbers is

${2}^{3} \times {3}^{2} \times 5 \times 7$

By expanding these values we get the answers as

$2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 7 \\ = 8 \times 9 \times 5 \times 7 \\ 72 \times 35 \\ = 2520$

The LCM of the numbers from 2 to 9 is found to be 2520

Hence, the LCM of the given numbers is found

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