Least Common Multiple (LCM) of 117 and 123
The least common multiple (LCM) of 117 and 123 is 4797.
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 117 and 123?
First, calculate the GCD of 117 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 123 = 0 remainder 117 |
| 2 | 123 ÷ 117 = 1 remainder 6 |
| 3 | 117 ÷ 6 = 19 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 60 | 4980 |
| 154 and 156 | 12012 |
| 161 and 100 | 16100 |
| 112 and 70 | 560 |
| 34 and 52 | 884 |