Least Common Multiple (LCM) of 76 and 139
The least common multiple (LCM) of 76 and 139 is 10564.
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 139?
First, calculate the GCD of 76 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 139 = 0 remainder 76 |
| 2 | 139 ÷ 76 = 1 remainder 63 |
| 3 | 76 ÷ 63 = 1 remainder 13 |
| 4 | 63 ÷ 13 = 4 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 128 | 10880 |
| 14 and 93 | 1302 |
| 108 and 91 | 9828 |
| 76 and 92 | 1748 |
| 189 and 78 | 4914 |