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 |
|---|---|
| 120 and 32 | 480 |
| 16 and 120 | 240 |
| 141 and 181 | 25521 |
| 17 and 112 | 1904 |
| 106 and 162 | 8586 |