Least Common Multiple (LCM) of 130 and 167
The least common multiple (LCM) of 130 and 167 is 21710.
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 130 and 167?
First, calculate the GCD of 130 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 167 = 0 remainder 130 |
| 2 | 167 ÷ 130 = 1 remainder 37 |
| 3 | 130 ÷ 37 = 3 remainder 19 |
| 4 | 37 ÷ 19 = 1 remainder 18 |
| 5 | 19 ÷ 18 = 1 remainder 1 |
| 6 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 71 | 7597 |
| 48 and 104 | 624 |
| 145 and 92 | 13340 |
| 98 and 172 | 8428 |
| 116 and 163 | 18908 |