Least Common Multiple (LCM) of 152 and 89
The least common multiple (LCM) of 152 and 89 is 13528.
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 89?
First, calculate the GCD of 152 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 89 = 1 remainder 63 |
| 2 | 89 ÷ 63 = 1 remainder 26 |
| 3 | 63 ÷ 26 = 2 remainder 11 |
| 4 | 26 ÷ 11 = 2 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 121 | 4477 |
| 72 and 191 | 13752 |
| 107 and 18 | 1926 |
| 72 and 133 | 9576 |
| 199 and 147 | 29253 |