Least Common Multiple (LCM) of 179 and 100
The least common multiple (LCM) of 179 and 100 is 17900.
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 179 and 100?
First, calculate the GCD of 179 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 100 = 1 remainder 79 |
| 2 | 100 ÷ 79 = 1 remainder 21 |
| 3 | 79 ÷ 21 = 3 remainder 16 |
| 4 | 21 ÷ 16 = 1 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 42 | 3318 |
| 71 and 186 | 13206 |
| 31 and 100 | 3100 |
| 168 and 130 | 10920 |
| 45 and 91 | 4095 |