Write the smallest number which is divisible by both 306 and 657.

Given: 306 and 657

To find: Here we have to find the smallest number which is divisible by both 306 and 657.

Solution:

The smallest number which is divisible by any two numbers is their LCM.

Now,

Writing the numbers as a product of their prime factors:

Prime factorisation of 306:

• $2\ \times\ 3\ \times\ 3\ \times\ 17\ =\ 2^1\ \times\ 3^2\ \times\ 17^1$

Prime factorisation of 657:

• $3\ \times\ 3\ \times\ 73\ =\ 3^2\ \times\ 73^1$

Multiplying the highest power of each prime number:

• $2^1\ \times\ 3^2\ \times\ 17^1\ \times\ 73^1\ =\ 22338$

LCM(306, 657)  $=$  22338

So, the smallest number which is divisible by both 306 and 657 is 22338.

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Updated on: 10-Oct-2022

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