Least Common Multiple (LCM) of 102 and 160
The least common multiple (LCM) of 102 and 160 is 8160.
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 160?
First, calculate the GCD of 102 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 160 = 0 remainder 102 |
| 2 | 160 ÷ 102 = 1 remainder 58 |
| 3 | 102 ÷ 58 = 1 remainder 44 |
| 4 | 58 ÷ 44 = 1 remainder 14 |
| 5 | 44 ÷ 14 = 3 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 86 | 4644 |
| 126 and 170 | 10710 |
| 135 and 96 | 4320 |
| 94 and 173 | 16262 |
| 72 and 122 | 4392 |