L.C.M AND H.C.F – basics, definition, formula, questions

L.C.M

L.C.M full form Least common multiple or Lowest Common Multiple which is exactly divisible by each one of the given numbers is called a L.C.M

For example

Find the lcm of 90,150,225,450,750,1125 ?

lcm and hcf question

ANSWER = 2250

H.C.F (or) G.C.D (OR) G.C.D

H.C.F full form Highest Common Factor (or) G.C.D full form Greatest common Division (or) G.C.M full form Greatest Common Measure of two or more than two numbers is greatest number that divides each of them exactly.

For example

Find the HCF of 90,150,225,450,750,1125 ?

lcm and hcf problems

ANSWER = 15

L.C.M OF FRACTIONS:
\text{L.C.M} = \frac{\text{L.C.M OF NUMERATORS}}{\text{H.C.F OF DEMONINATORS}} \\

For example

Find the lcm of \frac{1}{3},\frac{5}{6},\frac{2}{9},\frac{4}{27} \\

L.C.M of numerators = 1,5,2,4

\begin{array}{l|ll}
2 & 1,5,2,4 \\
\hline 2 & 1,5,1,2 \\
\hline 5 & 1,5,1,1 \\
\hline   & 1,1,1,1 \\
\end{array}

L.C.M of numerators = 2\times2\times5 = 20

H.C.F of demoninators = 3,6,9,27

\begin{array}{l|ll}
3 & 3,6,9,27 \\
\hline  & 1,2,3,9\\

\end{array}

H.C.F of demoninators = 3

\frac{\text{L.C.M OF NUMERATORS}}{\text{H.C.F OF DEMONINATORS}} = \frac{20}{3} \\

ANSWER =\frac{20}{3} \\

H.C.F OF FRACTION
\text{H.C.F} = \frac{\text{H.C.F OF NUMERATORS}}{\text{L.C.M OF DEMONINATORS}} \\

For example

Find the HCF of \frac{2}{3},\frac{8}{9},\frac{64}{81},\frac{10}{27} \\

H.C.F of numerators = 2,8,64,10

\begin{array}{l|ll}
2 & 2,8,64,10 \\
\hline  & 1,4,32,5 \\
\end{array}

H.C.F of numerators = 2

L.C.M of demoninators = 3,9,81,27

\begin{array}{l|ll}
3 & 3,9,81,27 \\
\hline 3 &1,3,27,9\\
\hline 3&1,1,9,3\\
\hline3&1,1,3,1\\
\hline &1,1,1,1\\
\end{array}

L.C.M of demoninators = 3\times3\times3\times3 = 81

\frac{\text{H.C.F OF NUMERATORS}}{\text{L.C.M OF DEMONINATORS}} = \frac{2}{81} \\

ANSWER =\frac{2}{81} \\

FACTOR METHOD

Find the factors of 1122.

\begin{array}{l|ll}
2 & 1122 \\
\hline 3 & 561 \\
\hline 11 & 187\\
\hline &17
\end{array}

ANSWER

Factor of 1122 = 2\times3\times11\times17

QUESTION 01

Find the L.C.M of 22,54,108,135,and198 is

ANSWER
\begin{array}{l|ll}
2 & 22,54,108,135,198 \\
\hline 11 & 11,27,54,135,99 \\
\hline 3 & 1,27,54,135,9\\
\hline 3 & 1,9,18,45,3 \\
\hline 3 & 1,3,6,15,1 \\
\hline 2 & 1,1,2,5,1 \\
\hline 5 &1,1,1,5,1 \\
\hline &1,1,1,1,1
\end{array}

L.C.M = 2\times11\times3\times3\times3\times2\times5 = 5940

QUESTION 02

Find the L.C.M of 30,60,90,and105 is

ANSWER
\begin{array}{l|ll}
3 & 30,60,90,105 \\
\hline 5 & 10,20,30,35 \\
\hline 2 & 2,4,6,7\\
\hline 2 & 1,2,3,7 \\
\hline 3 & 1,1,3,7 \\
\hline 7 & 1,1,1,7 \\
\hline  &1,1,1,1 \\

\end{array}

L.C.M = 3\times5\times2\times2\times3\times7 = 1260

QUESTION 03

Find the L.C.M of 0.48,1.08,and 2.80?

ANSWER

0.48\times100=48

1.08\times100=108

2.80\times100=280

The L.C.M of 48,108,280

\begin{array}{l|ll}
2 & 48,108,280 \\
\hline 2 & 24,54,140 \\
\hline 2 & 12,27,70\\
\hline 3 & 6,27,35 \\
\hline  & 2,9,35 \\

\end{array}

L.C.M = 2\times2\times2\times3\times2\times9\times35 =15120

L.C.M of 0.48,1.08,and 2.80 is 151.20

QUESTION 04

Find the H.C.F of 924,105, and 525 is

ANSWER
\begin{array}{l|ll}
3 & 924,105,525 \\
\hline 7 & 308,35,175 \\
\hline  & 44,5,25 \\
\end{array}

H.C.F = 3\times7 = 21

QUESTION 05

Find the H.C.F of 90,150 and 225 is

ANSWER
\begin{array}{l|ll}
5 & 90,150,225 \\
\hline 3 & 18,30,45 \\
\hline  & 6,10,15 \\
\end{array}

H.C.F = 5\times3 = 15

QUESTION 06

Find the H.C.F of 1651 and 2032

ANSWER
\begin{array}{l|ll}
127 & 1651,2032\\
\hline & 13,16 \\

\end{array}

H.C.F =127

QUESTION 07

Find the lcm of \frac{2}{20},\frac{4}{80},\frac{8}{40},\frac{16}{60} \\

ANSWER

L.C.M of numerators = 2,4,8,16

\begin{array}{l|ll}
2 & 2,4,8,16 \\
\hline 2 & 1,2,4,8 \\
\hline 2 & 1,1,2,4 \\
\hline 2 & 1,1,1,4 \\
\hline &amp: 1,1,1,1
\end{array}

L.C.M of numerators = 2\times2\times2[\times = 16

H.C.F of demoninators = 20,80,40,60

\begin{array}{l|ll}
5 & 20,80,40,60 \\
\hline   & 4,16,8,12\

\end{array}

H.C.F of demoninators = 5

\frac{\text{L.C.M OF NUMERATORS}}{\text{H.C.F OF DEMONINATORS}} = \frac{16}{5} \\

ANSWER =\frac{16}{5} \\

QUESTION 08

Find the HCF of \frac{6}{4},\frac{9}{16},\frac{21}{24},\frac{33}{32} \\

H.C.F of numerators = 6,9,21,33

\begin{array}{l|ll}
3 &6,9,21,33\\
\hline  &2,3,7,11 \\
\end{array}

H.C.F of numerators = 3

L.C.M of demoninators = 4,16,24,32

\begin{array}{l|ll}
4 & 4,16,24,32 \\
\hline 2 & 1,4,6,8\\
\hline 2&1,2,3,4\\
\hline2& 1,1,3,2\\
\hline 3&1,1,3,1\\
\hline & 1,1,1,1 \\
\end{array}

L.C.M of demoninators = 4\times2\times2\times2\times3 = 96

\frac{\text{H.C.F OF NUMERATORS}}{\text{L.C.M OF DEMONINATORS}} = \frac{3}{96} \\

=\frac{1}{32} \\

ANSWER =\frac{1}{32} \\

QUANTITATIVE APTITUDE STUDY MATERIAL

Ration and proportional

Simplification

Percentage

Number series

L.C.M and H.C.F

Simple Interest

Compound Interest

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