Least Common Multiple (LCM) of 100 and 117
The least common multiple (LCM) of 100 and 117 is 11700.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 100 and 117?
First, calculate the GCD of 100 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 117 = 0 remainder 100 |
| 2 | 117 ÷ 100 = 1 remainder 17 |
| 3 | 100 ÷ 17 = 5 remainder 15 |
| 4 | 17 ÷ 15 = 1 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 123 | 1722 |
| 113 and 122 | 13786 |
| 16 and 69 | 1104 |
| 80 and 25 | 400 |
| 198 and 74 | 7326 |