H.C.F. and L.C.M. of Decimals

Steps to solve H.C.F. and L.C.M. of decimals:

Step I: Convert each of the decimals to like decimals.

Step II: Remove the decimal point and find the highest common factor and least common multiple as usual.

Step III: In the answer (highest common factor /least common multiple), put the decimal point as there are a number of decimal places in the like decimals.


Now we will follow the step-by-step explanation on how to calculate the highest common factor and the least common multiple of decimals.


Worked-out examples on H.C.F. and L.C.M. of decimals:

1. Find the H.C.F. and the L.C.M. of 1.20 and 22.5

Solution:

Given, 1.20 and 22.5

Converting each of the following decimals into like decimals we get;

1.20 and 22.50

Now, expressing each of the numbers without the decimals as the product of primes we get

120 = 2 Γ— 2 Γ— 2 Γ— 3 Γ— 5 = 23 Γ— 3 Γ— 5

2250 = 2 Γ— 3 Γ— 3 Γ— 5 Γ— 5 Γ— 5 = 2 Γ— 32 Γ— 53

Now, H.C.F. of 120 and 2250 = 2 Γ— 3 Γ— 5 = 30
Therefore, the H.C.F. of 1.20 and 22.5 = 0.30 (taking 2 decimal places)

L.C.M. of 120 and 2250 = 23 Γ— 32 Γ— 53 = 9000
Therefore, L.C.M. of 1.20 and 22.5 = 90.00 (taking 2 decimal places)


2. Find the H.C.F. and the L.C.M. of 0.48, 0.72 and 0.108

Solution:

Given, 0.48, 0.72 and 0.108

Converting each of the following decimals into like decimals we get;

0.480, 0.720 and 0.108

Now, expressing each of the numbers without the decimals as the product of primes we get

480 = 2 Γ— 2 Γ— 2 Γ— 2 Γ— 2 Γ— 3 Γ— 5 = 25 Γ— 3 Γ— 5

720 = 2 Γ— 2 Γ— 2 Γ— 2 Γ— 3 Γ— 3 Γ— 5 = 24 Γ— 32 Γ— 5

108 = 2 Γ— 2 Γ— 3 Γ— 3 Γ— 3 = 22 Γ— 33

Now, H.C.F. of 480, 720 and 108 = 22 Γ— 3 = 12
Therefore, the H.C.F. of 0.48, 0.72 and 0.108 = 0.012 (taking 3 decimal places)

L.C.M. of 480, 720 and 108 = 25 Γ— 33 Γ— 5 = 4320
Therefore, L.C.M. of 0.48, 0.72, 0.108 = 4.32 (taking 3 decimal places)


3. Find the H.C.F. and the L.C.M. of 0.6, 1.5, 0.18 and 3.6

Solution:

Given, 0.6, 1.5, 0.18 and 3.6

Converting each of the following decimals into like decimals we get;

0.60, 1.50, 0.18 and 3.60

Now, expressing each of the numbers without the decimals as the product of primes we get

60 = 2 Γ— 2 Γ— 3 Γ— 5 = 22 Γ— 3 Γ— 5

150 = 2 Γ— 3 Γ— 5 Γ— 5 = 2 Γ— 3 Γ— 52

18 = 2 Γ— 3 Γ— 3 = 2 Γ— 32

360 = 2 Γ— 2 Γ— 2 Γ— 3 Γ— 3 Γ— 5 = 23 Γ— 32 Γ— 5

Now, H.C.F. of 60, 150, 18 and 360 = 2 Γ— 3 = 6
Therefore, the H.C.F. of 0.6, 1.5, 0.18 and 3.6 = 0.06 (taking 2 decimal places)

L.C.M. of 60, 150, 18 and 360 = 23 Γ— 32 Γ— 52 = 1800
Therefore, L.C.M. of 0.6, 1.5, 0.18 and 3.6 = 18.00 (taking 2 decimal places)

● Related Concept

● Decimals

● Decimal Numbers

● Decimal Fractions

● Like and Unlike Decimals

● Comparing Decimals

● Decimal Places

● Conversion of Unlike Decimals to Like Decimals

● Decimal and Fractional Expansion

● Terminating Decimal

● Non-Terminating Decimal

● Converting Decimals to Fractions

● Converting Fractions to Decimals

● H.C.F. and L.C.M. of Decimals

● Repeating or Recurring Decimal

● Pure Recurring Decimal

● Mixed Recurring Decimal

● BODMAS Rule

● BODMAS/PEMDAS Rules - Involving Decimals

● PEMDAS Rules - Involving Integers

● PEMDAS Rules - Involving Decimals

● PEMDAS Rule

● BODMAS Rules - Involving Integers

● Conversion of Pure Recurring Decimal into Vulgar Fraction

● Conversion of Mixed Recurring Decimals into Vulgar Fractions

● Simplification of Decimal

● Rounding Decimals

● Rounding Decimals to the Nearest Whole Number

● Rounding Decimals to the Nearest Tenths

● Rounding Decimals to the Nearest Hundredths

● Round a Decimal

● Adding Decimals

● Subtracting Decimals

● Simplify Decimals Involving Addition and Subtraction Decimals

● Multiplying Decimal by a Decimal Number

● Multiplying Decimal by a Whole Number

● Dividing Decimal by a Whole Number

● Dividing Decimal by a Decimal Number





7th Grade Math Problems

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