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Name
LOWEST COMMON MULTIPLE
(LCM)
We know that LCM is the least common multiple of two or more numbers
and it is calculated using prime factors.
Calculation of LCM is the process of finding the product of prime factors
counted the maximum number of times they occur in any of the numbers.
For example:
1. Prime factors of 10 = 2 × 5
2. Prime factors of 20 = 2 × 2 × 5
3. Prime factors of 30 = 2 × 3 × 5
4. Prime factors of 60 = 2 × 2 × 3 × 5
Quick Tip
To calculate the LCM of two or more numbers, we first the prime factors
of those numbers, then calculate the product of these factors counted the
maximum number of times they occur in any of the numbers. This product thus
obtained is the LCM of these numbers.
Let’s calculate the LCM of 12, 24 and 36. This can be calculated by two methods.
First method is common division method.
2
2
2
3
3
12, 24, 36
6, 12, 18
3, 6, 9
1, 1, 3
1, 1, 1
The factors have to be counted till we get 1 for each number.
Therefore, LCM = 2 × 2 × 2 × 3 × 3 = 72
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The other method is prime factorization method.
Prime factors of 12 = 2 × 2 × 3
Prime factors of 24 = 2 × 2 × 2 × 3
Prime factors of 36 = 2 × 2 × 3 × 3
Now the maximum occurrences of 2 are 2 × 2 × 2 in factors of 24 and 3 are
3 × 3 in 36. The product of 2 × 2 × 2 × 3 × 3 = 72.
Work it out...
A
Write the first 5 multiples of 111.
b
Whose sum is more? The number of multiples of 5 between 5 and 50 or the
number of multiples of 7 between 28 and 70.
c
Write the numbers whose multiple is 84.
d
Write all the factors of 28. Find the sum of these factors. What do you infer?
e
Calculate the LCM of following numbers by common division method.
a) 24, 40, 42
b) 15, 30, 60 c) 12, 60, 90
f
Find the LCM of the following numbers by prime factorization method.
a) 32, 42, 60
b) 15, 25, 60
c) 33, 55, 100
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