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 |
|---|---|
| 134 and 158 | 10586 |
| 86 and 20 | 860 |
| 129 and 183 | 7869 |
| 17 and 99 | 1683 |
| 20 and 75 | 300 |