Least Common Multiple (LCM) of 100 and 122
The least common multiple (LCM) of 100 and 122 is 6100.
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 122?
First, calculate the GCD of 100 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 122 = 0 remainder 100 |
| 2 | 122 ÷ 100 = 1 remainder 22 |
| 3 | 100 ÷ 22 = 4 remainder 12 |
| 4 | 22 ÷ 12 = 1 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 131 | 14017 |
| 39 and 13 | 39 |
| 113 and 39 | 4407 |
| 161 and 44 | 7084 |
| 42 and 172 | 3612 |