Least Common Multiple (LCM) of 100 and 74
The least common multiple (LCM) of 100 and 74 is 3700.
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 74?
First, calculate the GCD of 100 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 74 = 1 remainder 26 |
| 2 | 74 ÷ 26 = 2 remainder 22 |
| 3 | 26 ÷ 22 = 1 remainder 4 |
| 4 | 22 ÷ 4 = 5 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 57 | 1311 |
| 135 and 145 | 3915 |
| 80 and 111 | 8880 |
| 114 and 125 | 14250 |
| 13 and 94 | 1222 |