Least Common Multiple (LCM) of 76 and 90
The least common multiple (LCM) of 76 and 90 is 3420.
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 90?
First, calculate the GCD of 76 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 90 = 0 remainder 76 |
| 2 | 90 ÷ 76 = 1 remainder 14 |
| 3 | 76 ÷ 14 = 5 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 93 | 3999 |
| 176 and 120 | 2640 |
| 132 and 195 | 8580 |
| 11 and 73 | 803 |
| 140 and 197 | 27580 |