Least Common Multiple (LCM) of 158 and 102
The least common multiple (LCM) of 158 and 102 is 8058.
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 158 and 102?
First, calculate the GCD of 158 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 158 ÷ 102 = 1 remainder 56 |
| 2 | 102 ÷ 56 = 1 remainder 46 |
| 3 | 56 ÷ 46 = 1 remainder 10 |
| 4 | 46 ÷ 10 = 4 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 119 | 1309 |
| 16 and 89 | 1424 |
| 60 and 29 | 1740 |
| 55 and 160 | 1760 |
| 107 and 138 | 14766 |