Least Common Multiple (LCM) of 100 and 179
The least common multiple (LCM) of 100 and 179 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 100 and 179?
First, calculate the GCD of 100 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 179 = 0 remainder 100 |
| 2 | 179 ÷ 100 = 1 remainder 79 |
| 3 | 100 ÷ 79 = 1 remainder 21 |
| 4 | 79 ÷ 21 = 3 remainder 16 |
| 5 | 21 ÷ 16 = 1 remainder 5 |
| 6 | 16 ÷ 5 = 3 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 51 | 9078 |
| 52 and 163 | 8476 |
| 75 and 75 | 75 |
| 108 and 139 | 15012 |
| 105 and 170 | 3570 |