Least Common Multiple (LCM) of 102 and 69
The least common multiple (LCM) of 102 and 69 is 2346.
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 69?
First, calculate the GCD of 102 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 69 = 1 remainder 33 |
| 2 | 69 ÷ 33 = 2 remainder 3 |
| 3 | 33 ÷ 3 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 50 | 6850 |
| 102 and 56 | 2856 |
| 154 and 50 | 3850 |
| 119 and 98 | 1666 |
| 185 and 108 | 19980 |