Least Common Multiple (LCM) of 100 and 123
The least common multiple (LCM) of 100 and 123 is 12300.
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 123?
First, calculate the GCD of 100 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 123 = 0 remainder 100 |
| 2 | 123 ÷ 100 = 1 remainder 23 |
| 3 | 100 ÷ 23 = 4 remainder 8 |
| 4 | 23 ÷ 8 = 2 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 19 | 19 |
| 27 and 84 | 756 |
| 198 and 21 | 1386 |
| 28 and 192 | 1344 |
| 189 and 87 | 5481 |