Least Common Multiple (LCM) of 40 and 150
The least common multiple (LCM) of 40 and 150 is 600.
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 40 and 150?
First, calculate the GCD of 40 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 150 = 0 remainder 40 |
| 2 | 150 ÷ 40 = 3 remainder 30 |
| 3 | 40 ÷ 30 = 1 remainder 10 |
| 4 | 30 ÷ 10 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 150 | 1650 |
| 141 and 134 | 18894 |
| 82 and 115 | 9430 |
| 174 and 70 | 6090 |
| 180 and 32 | 1440 |