Least Common Multiple (LCM) of 85 and 152
The least common multiple (LCM) of 85 and 152 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 85 and 152?
First, calculate the GCD of 85 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 152 = 0 remainder 85 |
| 2 | 152 ÷ 85 = 1 remainder 67 |
| 3 | 85 ÷ 67 = 1 remainder 18 |
| 4 | 67 ÷ 18 = 3 remainder 13 |
| 5 | 18 ÷ 13 = 1 remainder 5 |
| 6 | 13 ÷ 5 = 2 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 107 | 7383 |
| 105 and 194 | 20370 |
| 182 and 148 | 13468 |
| 122 and 22 | 1342 |
| 120 and 57 | 2280 |