Least Common Multiple (LCM) of 76 and 187
The least common multiple (LCM) of 76 and 187 is 14212.
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 187?
First, calculate the GCD of 76 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 187 = 0 remainder 76 |
| 2 | 187 ÷ 76 = 2 remainder 35 |
| 3 | 76 ÷ 35 = 2 remainder 6 |
| 4 | 35 ÷ 6 = 5 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 32 | 1696 |
| 40 and 42 | 840 |
| 180 and 111 | 6660 |
| 197 and 62 | 12214 |
| 177 and 16 | 2832 |