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Find LCM of 18 and 27
A.44
B.54
C.34
D.24

Answer
VerifiedVerified
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Hint: We can find the LCM (lowest common multiple) by using prime factorization method. First find the prime factors of 18 and 27 respectively. Factors are the numbers which can divide the given number completely (no remainder is left). Then find the common factors from the given factors of 18 and 27. Find the smallest number from the common factors and you’ll have the least common multiple.

Complete step-by-step answer:
Here, given numbers are 18 and 27.
We have to find the LCM (lowest common multiple) of these numbers.
We can use factorization methods to find the LCM of these numbers.
First let us find the factors of both the numbers-
Factors are the numbers which can divide the given number completely (no remainder is left).
Now we know that18=2×9. We can further write it as- 18=2×3×3
Now we can write27=3×9 . We can further write it as- 27=3×3×3
 So we can write-
Factors of 18=2×3×3 and Factors of 27=3×3×3
So here we can see that 2×3 and 3×3 are the common factors of 18 and 27.
Now multiply the common factors to find the least common multiple-
LCM=2×3×3×3=54
So we can say that the Lowest common multiple of these numbers is 54.

Note: We can also find LCM by using formula –
The product of numbers=HCF× LCM-- (i)
We can find HCF by using the prime factorization method too. First let us find the factors of both the numbers-
Factors of 18=2×3×3 and Factors of 27=3×3×3
Then the highest factors are3 and3. On multiplying them we get,
HCF=3×3=9
On substituting the value of HCF and given numbers we get,
18×27=9×LCM
On solving we get,
LCM=2×27=54


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