Least Common Multiple (LCM) of 45 and 150
The least common multiple (LCM) of 45 and 150 is 450.
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 150?
First, calculate the GCD of 45 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 150 = 0 remainder 45 |
| 2 | 150 ÷ 45 = 3 remainder 15 |
| 3 | 45 ÷ 15 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 160 | 2080 |
| 71 and 85 | 6035 |
| 130 and 105 | 2730 |
| 130 and 53 | 6890 |
| 174 and 187 | 32538 |