Least Common Multiple (LCM) of 100 and 17
The least common multiple (LCM) of 100 and 17 is 1700.
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 17?
First, calculate the GCD of 100 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 17 = 5 remainder 15 |
| 2 | 17 ÷ 15 = 1 remainder 2 |
| 3 | 15 ÷ 2 = 7 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 23 | 414 |
| 163 and 72 | 11736 |
| 112 and 108 | 3024 |
| 32 and 105 | 3360 |
| 173 and 179 | 30967 |