Least Common Multiple (LCM) of 105 and 76
The least common multiple (LCM) of 105 and 76 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 105 and 76?
First, calculate the GCD of 105 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 76 = 1 remainder 29 |
| 2 | 76 ÷ 29 = 2 remainder 18 |
| 3 | 29 ÷ 18 = 1 remainder 11 |
| 4 | 18 ÷ 11 = 1 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 83 | 4980 |
| 159 and 70 | 11130 |
| 81 and 49 | 3969 |
| 141 and 194 | 27354 |
| 138 and 61 | 8418 |