Problems on LCM
Problems on LCM Shortcut Tricks
Common Multiple: Defined as number which is exactly divisible by each of the numbers under consideration. Example 60 is a common multiple of 2,3,4,5,6,10,15,20 and 30
Lowest Common Multiple(LCM): LCM of two or more numbers is the least or smallest number which is exactly divisible by each of them.
Find out LCM of 12, 16
Methods of Finding LCM
Method of Prime Factors
- Step-1 Resolve each of the given numbers into prime factors
- Step-2 Find the product of the highest powers of all the factors that occour in the resolution of the given number. This product will be required LCM
Find the LCM of 8, 12, 15 and 21
8= 2*2*2= 2^3 12= 2*2*3= 2^2*3 15=3*5 21=3*7 So Product of prime numbers with highest powers (2^3)*3*5*7=840 required LCM
Short Cut Method
Write down the given numbers in a line separating them by commas. Divide by any one of prime numbers 2, 3,5,7 which al least exactly divide at least any two of the given numbers . Repeat down the process untill you get a line of prime numbers. Now the product of all divisors and the numbers in the last line will be the required LCM.