Lowest Common Multiples is such a number which is exactly divisible by all of the numbers that are taken into consideration.

To find out the LCM, we observe the multiplication tables of each numbers that are considered.

In order to find the LCM of 4 and 8, we take,

Multiplication of 4 are 4,8,12,16,20,...
Multiplication of 8 are 8,16,24,32,40,....

The lowest common number in multiples of both 4 and 8 is 8 so, the LCM of 4 and 8 is 8.

Otherwise you can also find it using the HCF.

We know, HCF of 4 and 8 is 4.

LCM = 4×8/HCF
= 4×8/4
= 8

In other words, LCM × HCF = Number1 × Number2
Both HCF and LCM should be of the two numbers Number1 and Number2.


Exercise 8.2

General Section

1. Find the L.C.M. of the following expressions.

b) 4x³(x-3)(x+2) and 6x²(x+2)(x+3)

d) (x+2)(x+3), (x+3)(x-2), and (x-2)(x-3)



2. Find the L.C.M. of the following expressions.

b) ax² +ax, and ax² -a

d) x² -xy, and x³y -xy³

f) a³ -b³, and a² +ab +b²

h) x² -9, and 3x³ +81

j) x⁴ +x²y² +y⁴ and x³ -y³

l) 6x² -x -1 and 54x⁴ +2x


Creative Section

3. Find the L.C.M. of the following expressions.

b) (a-3)², (a-9) and (a³+27)

d) x⁴-y⁴, x²-y², and x³-y³

f) x³ -9x, x⁴ -2x³ -3x², and x³ -27

h) a⁴+a²+1, a³-1, and a³-a²+a

j) x³ -2x²y +2xy² -y³, x⁴ -y⁴, and x³ +y³

l) 2x³ +2x² -12x, 6x³ -6x² -72x, and 4x³ -24x² +32x



About vedanta EXCEL in MATHEMATICS Book 10

Author: Hukum Pd. Dahal
Editor: Tara Bahadur Magar

Vanasthali, Kathmandu, Nepal
+977-10-4382404, 01-4362082
vedantapublication@gmail.com


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Class 10 - Lowest Common Multiples Solved Exercises | vedanta EXCEL in MATHEMATICS is a collection of the solutions related to LCM for Nepal's Secondary Education Examination (SEE) appearing students.

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