Least Common Multiple (LCM) of 51 and 62
The least common multiple (LCM) of 51 and 62 is 3162.
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 51 and 62?
First, calculate the GCD of 51 and 62 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 62 = 0 remainder 51 |
| 2 | 62 ÷ 51 = 1 remainder 11 |
| 3 | 51 ÷ 11 = 4 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 178 | 18690 |
| 86 and 188 | 8084 |
| 82 and 37 | 3034 |
| 181 and 57 | 10317 |
| 177 and 20 | 3540 |