Least Common Multiple (LCM) of 160 and 102
The least common multiple (LCM) of 160 and 102 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 160 and 102?
First, calculate the GCD of 160 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 102 = 1 remainder 58 |
| 2 | 102 ÷ 58 = 1 remainder 44 |
| 3 | 58 ÷ 44 = 1 remainder 14 |
| 4 | 44 ÷ 14 = 3 remainder 2 |
| 5 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 161 | 10465 |
| 110 and 157 | 17270 |
| 120 and 100 | 600 |
| 147 and 129 | 6321 |
| 180 and 168 | 2520 |