# 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 × 2 × 2 × 3 × 5 = 23 × 3 × 5

2250 = 2 × 3 × 3 × 5 × 5 × 5 = 2 × 32 × 53

Now, H.C.F. of 120 and 2250 = 2 × 3 × 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 × 32 × 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 × 2 × 2 × 2 × 2 × 3 × 5 = 25 × 3 × 5

720 = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 24 × 32 × 5

108 = 2 × 2 × 3 × 3 × 3 = 22 × 33

Now, H.C.F. of 480, 720 and 108 = 22 × 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 × 33 × 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 × 2 × 3 × 5 = 22 × 3 × 5

150 = 2 × 3 × 5 × 5 = 2 × 3 × 52

18 = 2 × 3 × 3 = 2 × 32

360 = 2 × 2 × 2 × 3 × 3 × 5 = 23 × 32 × 5

Now, H.C.F. of 60, 150, 18 and 360 = 2 × 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 × 32 × 52 = 1800
Therefore, L.C.M. of 0.6, 1.5, 0.18 and 3.6 = 18.00 (taking 2 decimal places)

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