📊 Ordering Fractions Using LCM

Example: Arrange these in ascending order (smallest to largest): 5/8, 3/4, 7/10

Step 1: As the denominators are different, find the LCM of the denominators first

The denominators are 8, 4, and 10. We find the LCM using the cake/ladder/factorization box method, where we divide the numbers by a prime number each time.

8, 4, 10

→ Divide all numbers by 2 (a prime number), as they are multiples of 2

4, 2, 5

→ Divide again by 2, as both 4 and 2 are multiples of 2. (5 is not divisible, so write it as it is)

2, 1, 5

→ No common prime factor left. Stop.

LCM = 2 × 2 × 2 × 5 = 40

Step 2: Convert all fractions to have the same denominator (40, the LCM)

Trick: LCM = 2 × 2 × 2 × 5 = 40 from step 1 can be used to find the number that the denominator of each fraction has to be multiplied with, to get the LCM.

5/8

... Multiply both the numerator (5) and the denominator (8) by 5,
as LCM = 40
= (2*2*2) * 5
= 8*5
= denominator * 5

= (5 × 5) / (8 × 5)

= 25/40

3/4

Multiply both the numerator (3) and the denominator (4) by 10,
as LCM = 40
= (2*2) * (2*5)
= 4 * 10

= (3 × 10) / (4 × 10)

= 30/40

7/10

... Multiply both the numerator (7) and the denominator (10) by 4,
as LCM = 40
= (2*2) * (2*5)
= 4 * 10

= (7 × 4) / (10 × 4)

= 28/40

Step 3: Compare the numerators

Compare: 25, 28, 30
Ascending order (smallest to largest): 25 < 28 < 30

Step 4: Write the answer using the original fractions

Since:
25/40 < 28/40 < 30/40

The correct ascending order is:
5/8, 7/10, 3/4

✔ Tip to Remember: When denominators are different, always make them the same using LCM. Then compare the numerators only!