Least Common Multiple (LCM) of 100 and 158
The least common multiple (LCM) of 100 and 158 is 7900.
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 100 and 158?
First, calculate the GCD of 100 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 158 = 0 remainder 100 |
| 2 | 158 ÷ 100 = 1 remainder 58 |
| 3 | 100 ÷ 58 = 1 remainder 42 |
| 4 | 58 ÷ 42 = 1 remainder 16 |
| 5 | 42 ÷ 16 = 2 remainder 10 |
| 6 | 16 ÷ 10 = 1 remainder 6 |
| 7 | 10 ÷ 6 = 1 remainder 4 |
| 8 | 6 ÷ 4 = 1 remainder 2 |
| 9 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 132 | 2244 |
| 12 and 88 | 264 |
| 126 and 14 | 126 |
| 150 and 167 | 25050 |
| 197 and 163 | 32111 |