Question

Find the HCF and LCM of:
234, 572

Answer 1

Divide 572 by 234.

Calculate: 572 ÷ 234 = 2 (quotient) with a remainder.

Remainder = 572 − (234 × 2) = 572 − 468 = 104.

Now, divide 234 by the remainder 104.

Calculate: 234 ÷ 104 = 2 (quotient) with a remainder.

Remainder = 234 − (104 × 2) = 234 − 208 = 26.

Now, divide 104 by the new remainder 26.

Calculate: 104 ÷ 26 = 4 (quotient) with a remainder.

Remainder = 104 − (26 × 4) = 104 − 104 = 0.

When the remainder becomes 0, the last divisor used is the HCF.

Thus, HCF(234, 572) = 26.

The relationship between HCF and LCM is given by:

HCF × LCM=Product of the two numbers

Therefore, we can rearrange this to find the LCM:

LCM = `"Product of the two numbers"/"HCF"`

Product = 234 × 572.

LCM = `(234 xx 572)/26`.

 First, calculate 234 × 572 = 134568.

Now divide by the HCF: `134568/26` = 5172.

HCF(234, 572) = 26

LCM(234, 572) = 5172