Least Common Multiple (LCM) of 23 and 130
The least common multiple (LCM) of 23 and 130 is 2990.
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 23 and 130?
First, calculate the GCD of 23 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 130 = 0 remainder 23 |
| 2 | 130 ÷ 23 = 5 remainder 15 |
| 3 | 23 ÷ 15 = 1 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 51 | 7854 |
| 192 and 109 | 20928 |
| 99 and 44 | 396 |
| 52 and 132 | 1716 |
| 74 and 196 | 7252 |