Least Common Multiple (LCM) of 100 and 85
The least common multiple (LCM) of 100 and 85 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 85?
First, calculate the GCD of 100 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 85 = 1 remainder 15 |
| 2 | 85 ÷ 15 = 5 remainder 10 |
| 3 | 15 ÷ 10 = 1 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 86 | 9718 |
| 105 and 150 | 1050 |
| 138 and 84 | 1932 |
| 153 and 18 | 306 |
| 40 and 88 | 440 |