Least Common Multiple (LCM) of 62 and 102
The least common multiple (LCM) of 62 and 102 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 62 and 102?
First, calculate the GCD of 62 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 62 ÷ 102 = 0 remainder 62 |
| 2 | 102 ÷ 62 = 1 remainder 40 |
| 3 | 62 ÷ 40 = 1 remainder 22 |
| 4 | 40 ÷ 22 = 1 remainder 18 |
| 5 | 22 ÷ 18 = 1 remainder 4 |
| 6 | 18 ÷ 4 = 4 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 105 | 17535 |
| 101 and 172 | 17372 |
| 120 and 199 | 23880 |
| 37 and 61 | 2257 |
| 107 and 56 | 5992 |