Sum of least common multiple -L.C.M
Factor: one number said to be a factor or measure of another when it divides the mother exactly. Thus 6 and 8 are factors 0f 48.
Multiple: a number is said to be a multiple of another when it is exactly divisible by the other. Thus 48 are a multiple of6 and 8.
Prime number: prime number is a number which has no factors except itself and unity. Thus 2,3,5,7,11,13,17 etc. are composite numbers.
Composite number: composite number is number which has other factors besides it self and unity. Thus 14,15,16,18 etc. are composite numbers.
Co- prime: two numbers are said to be prime to each other when they have no common factors except unity. Note that the co-primes need not necessarily be prime.
Thus 15 and 19 are co-prime. Similarly 15, 17 and 22 are co-primes.
Common multiple: a common multiple of two or more numbers is a number which is exactly divisible by each of them. Thus 12 is a common multiple of 2, 3, 4 and 6.
Least common multiple (L.M.C): the least common multiple of two or more given number is the least number which is exactly divisible by each of them.
Thus 20 is a common multiple of 2, 4, 5 and 10
40 is a common multiple of 2, 4, 5 and 10
80 is a common multiple of 2, 4, 5 and 10
But 20 is the least common multiple of 2, 4, 5 and 10. The least common multiple is otherwise known as the lowest common multiple.
L.C.M of decimals,
To find the L.C.M of the given numbers in which decimals are given, first of all we find out the L.C.M of numbers with out decimals. And then we see the number in which the decimal is given in the minimum digits from right to left. We put the decimal in our result which is equal to that number of digits.
Example: find the L.C.M of 0.16, 5.4 and 0. 0098
First of all, we find the L.C.M of 16, 54, and 98
Here L.C.M of 16, 54, 98, is 21168
In numbers 0, 16,5,4,0.0098, the minimum digits from right to left are 5.4.
Here, In 5.4 the decimal is given of one digit from right to left. So we put decimal in our result such that: - 21168 = 2116.8
L.C.M of fractions,
A c e
If __, __, ___ be the proper fractions, then their L.C.M
B d f
L.C.M of numerators A, c, e
__________________________
H.C.F of denominators B, d, f
1 3 4 5
Example (1) finds L.C.M of _, _, _ and ___
2 5 7 12
L.C.M of 1,3,4,5 60
L.C.M = ________________ = ____
H.C.H of 2, 5,7,12 1
5 8 12 8 20
Example (second) finds the L.C.M of 3, 3, 3, 3, and 3
20
Solution: L.C.M = 3
Note this point, it is important: In the base of the given number is same, then L.C.M of these numbers will be equal to the maximum power of these numbers.