Least Common Multiple (LCM) of 105 and 150
The least common multiple (LCM) of 105 and 150 is 1050.
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 105 and 150?
First, calculate the GCD of 105 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 150 = 0 remainder 105 |
| 2 | 150 ÷ 105 = 1 remainder 45 |
| 3 | 105 ÷ 45 = 2 remainder 15 |
| 4 | 45 ÷ 15 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 21 | 1680 |
| 151 and 89 | 13439 |
| 38 and 51 | 1938 |
| 112 and 166 | 9296 |
| 71 and 176 | 12496 |