Find the least number which when divided by 20, 24 and 36 leaves a remainder 18 in each case.
Answers
Step-by-step explanation:
The prime factors of 20,25,33 and 36 are
20=2^2*5
25=5*5
30=2*3*5
36=2*2*3*3
Thus LCM=2*2*3*3*5*5=900
In each case the remainder is 4
So the number= 900+4=904
Concept:
In mathematics, Least Common Multiple is referred to LCM by its entire name, whereas Highest Common Factor is referred to HCF its complete name. The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the H.C.F. describes the biggest factor existing between any given pair of two or more numbers. LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).
Two key techniques—the division method and the prime factorization approach—can be used to determine H.C.F. and L.C.M.
Given:
when divided by 20, 24 and 36 leaves a remainder 18 in each case.
Find:
Find the least number which when divided by 20, 24 and 36 leaves a remainder 18 in each case.
Solution:
The prime factors of 20,24and 36 are
20=2x2x5
24=2x2x2x3
36=2x2x3x3
Thus LCM=2x2x2x3x3x5=360
In each case the remainder is 18
So the number= 360+18=378
Therefore, the least number which when divided by 20, 24 and 36 leaves a remainder 18 in each case is 368
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