Answer:
Step-by-step explanation:
First of all, the term multiple needs to be defined.
When a number is multiplied by another number other then zero, we get the multiple as result.
i.e. Multiples of 2 are: 2, 4, 6, 8, 10
To find the Least Common Multiple of numbers, we list the multiples of those numbers and then the samllest factor that is common in both lists is chosen as least common multiple.
1. 10, 20
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80
Multiples of 20: 20, 40, 60, 80, 100
Least Common Multiple: 20
2. 3, 9
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27
Multiples of 9: 9, 18, 27, 36, 45
Least Common Multiple: 9
3. 12, 24
Multiples of 12: 12, 24, 36, 48, 60, 72
Multiples of 24: 24, 48, 72, 96
Least Common Multiple: 24
4. 25, 45
Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250
Multiples of 45: 45, 90, 135, 180, 225, 270, 315
Least Common Multiple: 225
5. 5, 10
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40
Multiples of 10: 10, 20, 30, 40, 50, 60
Least Common Multiple: 10
6. 49, 56
Multiples of 49: 49, 98,147, 196, 245, 294, 343, 392, 441
Multiples of 56: 56, 112, 168, 224, 280, 336, 392, 448
Least Common Multiple: 392
This method of finding LCM is brute force and requires more time.
Another method is by using GCD(Greatest Common Divisor). It is the greatest positive integer number which completely divides all the numbers in consideration.
The product of the numbers is divided by their GCD to find the LCM.
i.e. for Q6
GCF(49, 56) = 7
LCM(49,56)= (49*56)/7
=2744/7=392
