Least Common Multiple (LCM) of 152 and 170
The least common multiple (LCM) of 152 and 170 is 12920.
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 152 and 170?
First, calculate the GCD of 152 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 170 = 0 remainder 152 |
| 2 | 170 ÷ 152 = 1 remainder 18 |
| 3 | 152 ÷ 18 = 8 remainder 8 |
| 4 | 18 ÷ 8 = 2 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 100 | 1900 |
| 184 and 16 | 368 |
| 101 and 169 | 17069 |
| 182 and 142 | 12922 |
| 193 and 161 | 31073 |