Least Common Multiple (LCM) of 53 and 62
The least common multiple (LCM) of 53 and 62 is 3286.
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 62?
First, calculate the GCD of 53 and 62 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 62 = 0 remainder 53 |
| 2 | 62 ÷ 53 = 1 remainder 9 |
| 3 | 53 ÷ 9 = 5 remainder 8 |
| 4 | 9 ÷ 8 = 1 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 31 | 3379 |
| 98 and 21 | 294 |
| 141 and 188 | 564 |
| 24 and 53 | 1272 |
| 40 and 68 | 680 |