Least Common Multiple (LCM) of 53 and 85
The least common multiple (LCM) of 53 and 85 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 53 and 85?
First, calculate the GCD of 53 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 85 = 0 remainder 53 |
| 2 | 85 ÷ 53 = 1 remainder 32 |
| 3 | 53 ÷ 32 = 1 remainder 21 |
| 4 | 32 ÷ 21 = 1 remainder 11 |
| 5 | 21 ÷ 11 = 1 remainder 10 |
| 6 | 11 ÷ 10 = 1 remainder 1 |
| 7 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 152 | 7448 |
| 144 and 34 | 2448 |
| 110 and 182 | 10010 |
| 145 and 198 | 28710 |
| 161 and 200 | 32200 |