Least Common Multiple (LCM) of 100 and 139
The least common multiple (LCM) of 100 and 139 is 13900.
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 139?
First, calculate the GCD of 100 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 139 = 0 remainder 100 |
| 2 | 139 ÷ 100 = 1 remainder 39 |
| 3 | 100 ÷ 39 = 2 remainder 22 |
| 4 | 39 ÷ 22 = 1 remainder 17 |
| 5 | 22 ÷ 17 = 1 remainder 5 |
| 6 | 17 ÷ 5 = 3 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 62 | 11718 |
| 154 and 20 | 1540 |
| 46 and 85 | 3910 |
| 179 and 26 | 4654 |
| 146 and 176 | 12848 |