Least Common Multiple (LCM) of 76 and 105
The least common multiple (LCM) of 76 and 105 is 7980.
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 105?
First, calculate the GCD of 76 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 105 = 0 remainder 76 |
| 2 | 105 ÷ 76 = 1 remainder 29 |
| 3 | 76 ÷ 29 = 2 remainder 18 |
| 4 | 29 ÷ 18 = 1 remainder 11 |
| 5 | 18 ÷ 11 = 1 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 187 | 19822 |
| 161 and 145 | 23345 |
| 170 and 142 | 12070 |
| 147 and 87 | 4263 |
| 116 and 52 | 1508 |