How to Find HCF and LCM Easily (Step-by-Step Guide)

HCF = Highest Common Factor
GCD = Greatest Common Divisor

Example: Find HCF/GCD of 12 and 18

Method 1: List the factors

Factors of 12:
1, 2, 3, 4, 6, 12

Factors of 18:
1, 2, 3, 6, 9, 18

Common factors:
1, 2, 3, 6

The highest common factor is 6.

So:

HCF(12, 18) = GCD(12, 18) = 6

Euclidean algorithm

For larger numbers, this is faster.

Find GCD of 48 and 18:

48 ÷ 18 = 2 remainder 12
18 ÷ 12 = 1 remainder 6
12 ÷ 6 = 2 remainder 0

When the remainder becomes 0, the last non-zero remainder is the GCD.

Answer = 6

For Decimal Numbers

Example: HCF of 1.2 and 1.8

Step 1: Count decimal places

Both numbers have 1 decimal place.

Step 2: Multiply both by 10

1.2 × 10 = 12
1.8 × 10 = 18

Step 3: Find the HCF of 12 and 18

HCF = 6

Step 4: Divide by 10

6 ÷ 10 = 0.6

HCF of 1.2 and 1.8 = 0.6

Another example: 2.4 and 3.6

Multiply by 10:

2.4 → 24
3.6 → 36

HCF of 24 and 36 = 12

Divide by 10:

12 ÷ 10 = 1.2

So, HCF = 1.2.

If the numbers have different numbers of decimal places, multiply by enough powers of 10 to make all of them whole numbers.

For example:

1.25 and 2.5

Multiply both by 100:

1.25 → 125
2.5 → 250

HCF(125, 250) = 125

Then divide by 100:

HCF = 1.25.

LCM (Least Common Multiple)

It is the smallest positive number that is a multiple of two or more numbers.

Example: LCM of 4 and 6

Multiples of 4:
4, 8, 12, 16, 20, 24...

Multiples of 6:
6, 12, 18, 24...

The first number appearing in both lists is 12.

For Decimal Numbers

Example: LCM of 1.2 and 1.8

Step 1: Remove the decimals

Both have 1 decimal place, so multiply both by 10:

$1.2\times10=12$

$1.8\times10=18$

Step 2: Find LCM of 12 and 18

Multiples:

12 → 12, 24, 36, 48...
18 → 18, 36, 54...

So:

$LCM(12,18)=36$

Step 3: Divide by 10

Because we multiplied the original numbers by 10:

$36\div10=\boxed{3.6}$

Therefore:

$\boxed{LCM(1.2,1.8)=3.6}$

Search This Blog