Least Common Multiple (LCM) of 152 and 189
The least common multiple (LCM) of 152 and 189 is 28728.
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 189?
First, calculate the GCD of 152 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 189 = 0 remainder 152 |
| 2 | 189 ÷ 152 = 1 remainder 37 |
| 3 | 152 ÷ 37 = 4 remainder 4 |
| 4 | 37 ÷ 4 = 9 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 65 | 650 |
| 65 and 114 | 7410 |
| 148 and 178 | 13172 |
| 97 and 18 | 1746 |
| 120 and 180 | 360 |