Least Common Multiple (LCM) of 102 and 62
The least common multiple (LCM) of 102 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 102 and 62?
First, calculate the GCD of 102 and 62 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 62 = 1 remainder 40 |
| 2 | 62 ÷ 40 = 1 remainder 22 |
| 3 | 40 ÷ 22 = 1 remainder 18 |
| 4 | 22 ÷ 18 = 1 remainder 4 |
| 5 | 18 ÷ 4 = 4 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 123 | 1353 |
| 72 and 91 | 6552 |
| 150 and 150 | 150 |
| 146 and 52 | 3796 |
| 58 and 99 | 5742 |