Given that HCF(306, 657) = 9, find LCM(306, 657).
22338
We are given two numbers, 306 and 657, and their HCF (Highest Common Factor) is 9.
There is a standard relation between LCM and HCF of two numbers:
\( \text{LCM} \times \text{HCF} = \text{product of the two numbers} \)
We can use this relation to find the LCM when the HCF and the two numbers are known.
Step 1: Write the relation for our numbers
Here, the numbers are 306 and 657, and
\( \text{HCF} = 9 \)
So,
\( \text{LCM}(306, 657) \times 9 = 306 \times 657 \)
We want to find \( \text{LCM}(306, 657) \).
Step 2: Rearrange the formula to make LCM the subject
From
\( \text{LCM} \times 9 = 306 \times 657 \)
we get
\( \text{LCM}(306, 657) = \dfrac{306 \times 657}{9} \)
Step 3: Simplify the fraction
It is easier to first divide 306 by 9, instead of multiplying first and then dividing.
Compute:
\( 306 \div 9 = 34 \)
So the expression becomes:
\( \text{LCM}(306, 657) = 34 \times 657 \)
Step 4: Multiply 34 and 657
We multiply step by step using simple break-up.
Write 34 as \( 30 + 4 \).
First, calculate \( 657 \times 30 \).
\( 657 \times 30 = 657 \times 3 \times 10 \)
\( 657 \times 3 = 1971 \)
So,
\( 657 \times 30 = 1971 \times 10 = 19710 \)
Next, calculate \( 657 \times 4 \).
\( 657 \times 4 = 2628 \)
Now add these two results:
\( 19710 + 2628 = 22338 \)
So,
\( 34 \times 657 = 22338 \)
Step 5: Conclude the value of LCM
We have found:
\( \text{LCM}(306, 657) = 22338 \)
Therefore, the LCM of 306 and 657 is 22338.