Least Common Multiple (LCM) of 46 and 130
The least common multiple (LCM) of 46 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 46 and 130?
First, calculate the GCD of 46 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 130 = 0 remainder 46 |
| 2 | 130 ÷ 46 = 2 remainder 38 |
| 3 | 46 ÷ 38 = 1 remainder 8 |
| 4 | 38 ÷ 8 = 4 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 17 | 1428 |
| 131 and 104 | 13624 |
| 30 and 114 | 570 |
| 66 and 100 | 3300 |
| 39 and 143 | 429 |