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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.
Updated on: 10-Oct-2022
5K+ Views
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