# Lcm Of 12 And 15

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 (ab) is  zero.

## Methods For Finding Least Common Muliples:

Multiplication Method :
Step 1: Finding  the multiples of first number
Step 2:  Finding the multiples of second number
Step 3: Note  the common multiples for both numbers given.

Step 4: LCM for numbers given are  least common multiples

Division method:
Step 1: Dividing given numbers by common multiple
Step 2: Dividing till get zero or no divisor
Step 3: multiplying all factor then we get LCM

## Example Problems for LCM:

Example 1 :
Find the l.c.m. of , 12 and 15.

Solution :
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

Example 2:
Find the lowest common multiple of 12 and 15.

Solution:
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
Example 3:
Find lowest common multiple of 12

Solution:
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.

Example 3:
Find lowest common multiple of 15

Solution:
3 ¦15       (common divisor 3)
5 ¦5       ( no common divisor 5)
1

l.c.m. =  3× 5 = 15.

Example 4:

Solution:
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: