LEAST COMMON MULTIPLE (LCM) -
A common multiple is a number that is a multiple of two or more numbers.
The LEAST COMMON MULTIPLE (L.C.M) of two or more numbers is the smallest number that is a multiple of the given set of numbers.
1.) COMMON MULTIPLE METHOD OR LISTING METHOD : -
In this method,
§ STEP 1.) First we find the multiples (i.e. write the tables) of the given numbers separately.
§ STEP 2.) Then we underline the common multiples of the numbers and write it down.
§ STEP 3.) We select the smallest common multiple amongst the common multiples.
§ STEP 4.) The smallest common multiple is the L.C.M of the given numbers.
SOLVED EXAMPLE 1:
Find the L.C.M of 6, 8 and 12 using the listing method (common multiple method).
SOLUTION :-
§ 6, 8 and 12
STEP 1.) Write the tables up to 12 times.
Multiples of 6 are 6, 12, 18, 24 , 30, 36, 42, 48, 54, 60, 66, 72.
Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96.
Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144.
STEP 2.) Color Red and write the common multiples of 6, 8 and 12.
Common multiples are 24, 48, 72.
STEP 3.) Color Blue the smallest common multiple. This is the L.C.M
∴The L.C.M is 24.
Answer : The L.C.M of 6, 8 and 12 is 24. (Ans.)
PLEASE NOTE :-
§ In case we get one common multiple only, we have to find more multiples i.e. write the tables more say up to 15 times.
§ The L.C.M of two or more numbers is their smallest common multiple.