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 |
|---|---|
| 12 and 62 | 372 |
| 107 and 45 | 4815 |
| 19 and 182 | 3458 |
| 113 and 104 | 11752 |
| 177 and 133 | 23541 |