Least Common Multiple (LCM) of 76 and 100
The least common multiple (LCM) of 76 and 100 is 1900.
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 76 and 100?
First, calculate the GCD of 76 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 100 = 0 remainder 76 |
| 2 | 100 ÷ 76 = 1 remainder 24 |
| 3 | 76 ÷ 24 = 3 remainder 4 |
| 4 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 140 | 7980 |
| 118 and 163 | 19234 |
| 113 and 14 | 1582 |
| 85 and 50 | 850 |
| 116 and 100 | 2900 |