Least Common Multiple (LCM) of 101 and 122
The least common multiple (LCM) of 101 and 122 is 12322.
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 101 and 122?
First, calculate the GCD of 101 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 122 = 0 remainder 101 |
| 2 | 122 ÷ 101 = 1 remainder 21 |
| 3 | 101 ÷ 21 = 4 remainder 17 |
| 4 | 21 ÷ 17 = 1 remainder 4 |
| 5 | 17 ÷ 4 = 4 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 142 | 22010 |
| 67 and 137 | 9179 |
| 27 and 113 | 3051 |
| 113 and 45 | 5085 |
| 97 and 111 | 10767 |