Least Common Multiple (LCM) of 150 and 170
The least common multiple (LCM) of 150 and 170 is 2550.
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 150 and 170?
First, calculate the GCD of 150 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 170 = 0 remainder 150 |
| 2 | 170 ÷ 150 = 1 remainder 20 |
| 3 | 150 ÷ 20 = 7 remainder 10 |
| 4 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 174 | 4350 |
| 67 and 146 | 9782 |
| 153 and 55 | 8415 |
| 87 and 128 | 11136 |
| 134 and 125 | 16750 |