How to Find HCF and LCM of Decimal Numbers
Find HCF and LCM of decimal numbers by padding, scaling to integers, and descaling, with a worked example and practice questions with answers.
Expected Interview Answer
HCF and LCM of decimals are found by converting every number to have the same number of decimal places, treating them as whole integers to compute HCF/LCM by the usual method, then reinserting the decimal point in the same position as in the original numbers.
The key insight is that multiplying every given decimal by the same power of 10 (enough to clear all decimal points) does not change the underlying ratio relationships between the numbers, so the HCF and LCM of the resulting integers can be scaled back down by dividing by that same power of 10. Padding shorter decimals with trailing zeros first, so every number has an equal count of decimal digits, is essential — comparing 0.4 and 0.04 directly is error-prone, but 0.40 and 0.04 padded equally makes the integer conversion (40 and 4) clean. After computing HCF or LCM of the padded integers using the standard prime-factorization or division method, divide the result by the same power of 10 used to convert, and the decimal point lands in the correct place automatically.
- Reduces decimal HCF/LCM to a well-known integer HCF/LCM procedure
- Equal decimal-place padding avoids the most common conversion error
- The same scale factor used to convert is reused to convert the answer back
AI Mentor Explanation
Comparing partnership run rates of 4.2 and 0.35 runs per ball is confusing directly, but padding both to two decimal places — 4.20 and 0.35 — and multiplying by 100 converts them to clean integers 420 and 35, whose HCF (35) is found the standard way. Dividing that HCF back by 100 gives 0.35 as the decimal HCF, exactly the padding-scale-descale routine used for any decimal HCF or LCM. The padding step is what prevents a scorer from misreading 4.2 as having “fewer digits” than 0.35 and miscomputing the ratio.
Worked example
Pad and scale
- 1.20, 0.36 → ×100 → 120, 36
Integer HCF/LCM
- HCF(120,36) = 12
- LCM(120,36) = 360
Descale
- HCF = 12/100 = 0.12
- LCM = 360/100 = 3.6
Step-by-Step Explanation
Step 1
Equalize decimal places
Pad shorter decimals with trailing zeros so all numbers have the same digit count after the point.
Step 2
Scale to integers
Multiply every number by the matching power of 10 to remove the decimal point.
Step 3
Compute HCF/LCM normally
Apply the standard integer HCF (division/prime factorization) or LCM method.
Step 4
Descale the result
Divide the resulting HCF or LCM by the same power of 10 used for scaling.
What Interviewer Expects
- Correct padding of decimals to equal place counts before scaling
- Correct choice of power of 10 to convert to integers
- Accurate standard HCF/LCM computation on the resulting integers
- Correct descaling to restore the decimal point in the final answer
Common Mistakes
- Computing HCF/LCM on decimals without first padding to equal decimal places
- Using different scale factors for different numbers in the same problem
- Forgetting to descale the final HCF or LCM back to decimal form
- Confusing the padding step (adding zeros) with actually changing the number’s value
Best Answer (HR Friendly)
“I first pad every decimal with trailing zeros so they all have the same number of digits after the decimal point, then multiply all of them by the matching power of ten to turn them into plain integers. From there I find the HCF or LCM exactly the way I would for whole numbers, and finally I divide that result by the same power of ten I used to scale up, which puts the decimal point back in the right place.”
Follow-up Questions
- How would you find the HCF of a mix of decimals with different numbers of decimal places, like 2.5 and 0.125?
- How does the LCM of decimals relate to finding a common recurring event, like two timers that both hit whole values?
- Why must the same power of 10 be used to scale every number in the set?
- How would you verify a computed decimal HCF is correct by checking divisibility?
MCQ Practice
1. Find the HCF of 0.63 and 1.05.
Scale by 100: 63 and 105. HCF(63,105) = 21. Descale: 21/100 = 0.21.
2. Find the LCM of 1.5 and 0.6.
Pad and scale by 10: 15 and 6. LCM(15,6) = 30. Descale by dividing by 10: 30/10 = 3.0.
3. Why must all decimals be padded to the same number of decimal places before scaling to integers?
A single scale factor (power of 10) only produces integers for every number if they all share the same decimal-place count.
Flash Cards
First step for decimal HCF/LCM? — Pad all decimals with trailing zeros to equal decimal-place counts.
Second step? — Multiply all numbers by the same power of 10 to convert to integers.
Third step? — Compute HCF or LCM using the standard integer method.
Final step? — Divide the result by the same power of 10 used for scaling, to restore the decimal point.