Least Common Multiple (LCM) of 69 and 130
The least common multiple (LCM) of 69 and 130 is 8970.
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 69 and 130?
First, calculate the GCD of 69 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 130 = 0 remainder 69 |
| 2 | 130 ÷ 69 = 1 remainder 61 |
| 3 | 69 ÷ 61 = 1 remainder 8 |
| 4 | 61 ÷ 8 = 7 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 96 | 4896 |
| 58 and 21 | 1218 |
| 10 and 46 | 230 |
| 193 and 174 | 33582 |
| 94 and 81 | 7614 |