Least Common Multiple (LCM) of 85 and 53
The least common multiple (LCM) of 85 and 53 is 4505.
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 53?
First, calculate the GCD of 85 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 53 = 1 remainder 32 |
| 2 | 53 ÷ 32 = 1 remainder 21 |
| 3 | 32 ÷ 21 = 1 remainder 11 |
| 4 | 21 ÷ 11 = 1 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 32 | 2400 |
| 61 and 157 | 9577 |
| 26 and 126 | 1638 |
| 178 and 12 | 1068 |
| 158 and 129 | 20382 |