Least Common Multiple (LCM) of 100 and 170
The least common multiple (LCM) of 100 and 170 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 170?
First, calculate the GCD of 100 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 170 = 0 remainder 100 |
| 2 | 170 ÷ 100 = 1 remainder 70 |
| 3 | 100 ÷ 70 = 1 remainder 30 |
| 4 | 70 ÷ 30 = 2 remainder 10 |
| 5 | 30 ÷ 10 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 30 | 690 |
| 180 and 83 | 14940 |
| 168 and 35 | 840 |
| 104 and 116 | 3016 |
| 135 and 153 | 2295 |