Mohan sold crackers in a packs of 22 and 40 each. If he wants full packs of both and
the same number of crackers of each kind, how many packs of each would he need to buy?
Answers
Answer:
Step-by-step explanation:
GIVEN :
Total number of Packs brought by Mohan = 22 + 40
In first pack of crackers he bought = 22
In second pack of crackers he bought = 40
TO FIND :
The numbers of pack of crackers of each he needs to buy = ?
STEP - BY - STEP EXPLAINATION :
⇒ First pack of crackers he bought = 22 (GIVEN)
⇒ Second pack of crackers he bought = 40 (GIVEN)
⇒ STEP 1 : Here firstly we'll have to find the LCM ( Lowest common Multiple ) of 22 and 40 = ?
⇒ STEP 2 : So, let's find the LCM of 22 and 40
⇒ STEP 3 :
When we'll find LCM with GCF ( Greatest common factor ) method :
⇒ GCF (22,40) = 2
⇒ LCM(22,40) = ( 22 × 40) / 2
⇒LCM(22,40) = 880 / 2
⇒ LCM(22,40) = 440\
Therefore, after finding LCM with GCF method we get here LCM of 20 and 44 as 440.
Now we'll find the LCM of 22 and 40 by Prime factorization method :
⇒ 22 = × ( 2 × 11 × 11 )
⇒ Prime factors of 22 are as follows we get here 2 and 11
⇒ 40 = × ( 2 × 2 × 2 × 5 )
⇒ Prime factors of 40 are as follows we get here 2 and 5
⇒ LCM(22,40) = × × ( 2 × 2 × 2 × 11 × 5 )
⇒ LCM(22,40) = 440
( NOTE : You can apply any of the methods whether it's GCF method or LCM method )
Therefore the LCM of 22 and 40 is 440