Least Common Multiple (LCM) of 102 and 58
The least common multiple (LCM) of 102 and 58 is 2958.
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 58?
First, calculate the GCD of 102 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 58 = 1 remainder 44 |
| 2 | 58 ÷ 44 = 1 remainder 14 |
| 3 | 44 ÷ 14 = 3 remainder 2 |
| 4 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 20 | 420 |
| 54 and 150 | 1350 |
| 40 and 150 | 600 |
| 183 and 109 | 19947 |
| 80 and 122 | 4880 |