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LCM stands for ‘Least Common Multiple’. It is thus the smallest number which gets exactly divisible by the given two or more numbers. If we had to find the then LCM of two numbers say a and b. Then L(a,b) is the least positive integer which gets divisible by both a and b.
For example: Find the LCM of 4 and 12.
Solution:
Multiples of 4= 4, 8, 12,16, 20, 24, 28, 32, 36, ……
Multiples of 12= 12, 24, 36, 48, 60, 72, 84, ……
Common Multiples= 12, 24, 36, …….
Least Common Multiple= L(4, 12)= 12
HCF stand for ‘Highest Common Factor’. Hence, it is the greatest factor that exists between given two or more than two numbers. Or as we may say, it is the highest positive integer H(a, b) dividing two or more than two numbers (here, a and b) without leaving any remainder.
For example: Find the HCF of 144 and 104.
Solution:
Factors of 144= 2 x 2 x 2 x 2 x 3 x 3
Factors of 104= 2 x 2 x 2 x 13
Highest Common Factor= H(144, 104)= 2 x 2 x 2 = 8