The smallest numbers of common multiples for two numbers is called their least common multiple.LCM is almost GCF evaluation but for greatest number here we are
finding lowest common multiple. There are two methods for finding LCM which are multiplication method and division method.LCM for given numbers is used in
fraction additions and simplifications.The product of greatest common diviosrs (GCD) and Least common multiple (LCM) of two numbers is equal to the product of given numbers. the **least common multiple** (LCM) when two integers *a* and *b* is a smallest positive integer which is multiple of both of
*a* and *b*. which can be divided by *a* and *b* without a remainder. If *a* or *b* will be 0, then there will be no such positive integer,
then LCM for (*a*, *b*) is zero.

**Step 4:** LCM for numbers given are least common multiples

Find the l.c.m. of , 12 and 15.

Multiples of 12 : 12, 24 , 36, 48 , 60, 72 , 84

Multiples of 15: 15,30,45,60,75,90

Common multiples factor: 60

Lowest common multiples: 60

Find the lowest common multiple of 12 and 15.

3¦ 12,15 (common divisor 3)

4¦ 4,5 ( no common divisor 4)

5¦ 1,5(no common divisor 5)

1,1

l.c.m. = 3×4×5 = 60

Find lowest common multiple of 12

2 ¦12 (common
divisor 2)

2 ¦6
(common divisor 2)

3 ¦3 (common divisor 3)

1 (No common divisor)

l.c.m. = 2 × 2 × 3 = 12.

Find lowest common multiple of 15

3 ¦15 (common
divisor 3)

5 ¦5
( no common divisor 5)

1

l.c.m. = 3× 5 = 15.

Add` 5/12 + 2/15`

For adding two unlike fractions we take LCM for 12, 15 are 60

`5/12 +2/15` = `(5*5)/(12*5) +(2*4)/(15*4)`
(multiply denominator with number which get LCM)

=`25/60+8/60`

=`33/60`

Example 5:

Add` 7/12 + 1/15`

Solution:

For adding two unlike fractions we take LCM for 12, 15 are 60

`7/12 +1/15` = `(7*5)/(12*5) +(1*4)/(15*4)`
(multiply denominator with number which get LCM)

=`35/60+4/60`

=`39/60`