LCM of Decimal Numbers

The process involves converting the decimals into whole numbers by equalizing the number of decimal places, finding the LCM of these whole numbers, and finally adjusting the result by the decimal places.

1. Multiply the decimal numbers by a power of 10 to convert the decimals to whole numbers.
2. Find the LCM of these whole numbers.
3. Adjust by the appropriate power of 10 based on the number of decimal places by dividing the LCM you obtained by the same power of 10 that you used in step 1.

Solved Examples on LCM of Decimal Numbers

Example 1: Finding LCM of 3, 2.7, and 0.09

Solution: Convert to Whole Numbers:
3.00, 2.70, 0.09 (2 decimal places for all)

Calculate the Multiplier: n = 10² = 100

Remove Decimal Points: 300, 270, 9

Prime Factorization:

300 = 2² × 3¹ × 5²
270 = 2¹ × 3³ × 5¹
9 = 3²

Calculate LCM:
LCM(300, 270, 9) = 2max⁡(2,1,0) × 3max⁡(1,3,2) × 5max⁡(2,1,0) = 2² × 3³ × 5² = 2700

Adjust Result:

LCM (3.00, 2.70, 0.09)= 2700 / 100 = 27

Example 2: Finding LCM of 0.216, 6, and 2

Solution: Convert to Whole Numbers:
0.216 = 216
6.000 = 6000
2.000 = 2000

Calculate the Multiplier: n = 10³ = 1000

Remove Decimal Points: 216, 6000, 2000

Prime Factorization:
216 = 2³ x 3
6000 = 2⁴ × 3¹ × 5
2000 = 2⁴ × 5³

Calculate LCM:
LCM(216, 6000, 2000) = 2max⁡(3,4,4) × 3max⁡(3,1,0) × 5max⁡(0,3,3) = 2⁴ × 3³ × 5³ = 54000

Adjust Result:
LCM ( 0.216, 6, 2) = 54

Please refer HCF of Decimal Numbers for finding HCF of Decimal Numbers

Practice Questions on Finding the LCM and HCF of Decimal Numbers

Question 1: Find the LCM and HCF of 0.5, 2.5, and 0.1.

Question 2: Calculate the LCM and HCF of 1.2, 0.4, and 0.6.

Question 3: Determine the LCM and HCF of 0.45 and 1.35.

Question 4: Find the LCM and HCF of 4.8, 1.6, and 2.4.

Question 5: Calculate the LCM and HCF of 0.75 and 3.5.

Related Articles:

• HCF and LCM of polynomials
• HCF and LCM of fractions
• LCM of Polynomials