Least Common Multiple (LCM) of 100 and 76
The least common multiple (LCM) of 100 and 76 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 100 and 76?
First, calculate the GCD of 100 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 76 = 1 remainder 24 |
| 2 | 76 ÷ 24 = 3 remainder 4 |
| 3 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 189 | 30996 |
| 191 and 114 | 21774 |
| 27 and 71 | 1917 |
| 90 and 160 | 1440 |
| 30 and 136 | 2040 |