Least Common Multiple (LCM) of 101 and 123
The least common multiple (LCM) of 101 and 123 is 12423.
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 123?
First, calculate the GCD of 101 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 123 = 0 remainder 101 |
| 2 | 123 ÷ 101 = 1 remainder 22 |
| 3 | 101 ÷ 22 = 4 remainder 13 |
| 4 | 22 ÷ 13 = 1 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 31 | 6169 |
| 200 and 24 | 600 |
| 40 and 83 | 3320 |
| 122 and 87 | 10614 |
| 102 and 194 | 9894 |