Least Common Multiple (LCM) of 45 and 130
The least common multiple (LCM) of 45 and 130 is 1170.
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 45 and 130?
First, calculate the GCD of 45 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 130 = 0 remainder 45 |
| 2 | 130 ÷ 45 = 2 remainder 40 |
| 3 | 45 ÷ 40 = 1 remainder 5 |
| 4 | 40 ÷ 5 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 14 | 1400 |
| 107 and 31 | 3317 |
| 194 and 179 | 34726 |
| 123 and 27 | 1107 |
| 104 and 12 | 312 |