find the LCM of the following number a) 9 and 4 b) 12 and 5 c) 6 and 5 d) 15 and 4 Observe a common property in the obtained LCM s . Is LCM the product of two number in each case ? class 6th
Answers
Step-by-step explanation:
a) Given numbers are 4 and 9.
To find out: The least common multiple (LCM) of the two numbers.
The prime factor of 4 is 2 and that of 9 is 3.
Hence, 4 and 9 can be represented as the product of their prime factors as:
4=2×2=2
2
9=3×3=3
2
We know that the LCM of two or more numbers is the product of the highest powers of all the unique factors.
∴ LCM(4,9)=2
2
×3
2
=36
Hence, the least common multiple of 4 and 9 is 36.
b) LCM=2×2×3×5=60.
2 ∣
12,5
2 ∣
6,5
3 ∣
3,5
5 ∣
1,5
1,1
Yes, it can be observed that in each case, the LCM of the given numbers is the product of these numbers. When two numbers are co-prime, their LCM is the product of those numbers. Also, in this case, LCM is a multiple of 3.
c) LCM=2×3×4=30
2 ∣
6,5
3 ∣
3,5
5 ∣
1,5
1,1
Yes, it can be observed that in each case, the LCM of the given numbers is the product of these numbers. When two numbers are co-prime, their LCM is the product of those numbers. Also, in this case, LCM is a multiple of 3.
d) LCM=2×2×3×5=60.
Yes, it can be observed that in each case, the LCM of the given numbers is the product of these numbers. When two numbers are co-prime, their LCM is the product of those numbers. Also, in this case, LCM is a multiple of 3.
2 ∣
15,4
2 ∣
15,2
3 ∣
15,1
5 ∣
5,1
1,1