Least common multiple of three numbers

L.C.M is the Smallest number that a set of given numbers divides evenly into It is useful to know how to do this so you can find a common denominator when adding or subtracting or ordering fractions. Least common multiple of three numbers can be calculated using two methods Prime factorization Ladder Method or L Method

Example1: Find L.C.M of 6 , 12 , 15 Solution Method 1:- Prime Factorization Method Step1:- Find prime factorization of 6 , 12 and 15 12 15 6 2 6 3 5 2 3 2 3 6 = 2 x 3 12 = 2 x 2 x 3 15 = 3 x 5 Step2:- Write down product of all the common factors Step 3:- Write down product of all remaining factors L.C.M = 2 x 3 x 2 x 5 = 60

Solution Method 2:- L Method Step1:- Use L Method to find factors of 6 , 12 and 15 3 6 12 15 Common Factors Once 2 2 4 5 1 2 5 Step2:- Write down product of all the common factors Step 3:- Write down product of all remaining factors Remaining Factors L.C.M = 3 x 2 x 1 x 2 x 5 = 60

Example2: Find L.C.M of 18 , 24 , 60 Solution Method 1:- Prime Factorization Method Step1:- Find prime factorization of 18 , 24 , 60 24 60 18 2 12 2 30 2 9 2 6 2 15 3 3 2 3 3 5 18 = 2 x 3 x 3 24 = 2 x 2 x 2 x 3 60 = 2 x 2 x 3 x 5

18 = 2 x 3 x 3 24 = 2 x 2 x 2 x 3 60 = 2 x 2 x 3 x 5 Step2:- Write down product of all the common factors Step 3:- Write down product of all remaining factors L.C.M = 2 x 3 x 2 x 3 x 2 x 5 = 360

Solution Method 2:- L Method Step1:- Use L Method to find factors of 18 , 24 , 60 2 18 24 60 Common Factors Once 3 9 12 30 2 3 4 10 3 2 5 Remaining Factors Step2:- Write down product of all the common factors Step 3:- Write down product of all remaining factors L.C.M = 2 x 3 x 2 x 3 x 2 x 5 = 360

Try these Find L.C.M of 36 , 18, 9 Find L.C.M of 20 , 30, 50