Least Common Multiple (LCM) of 51 and 139
The least common multiple (LCM) of 51 and 139 is 7089.
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 51 and 139?
First, calculate the GCD of 51 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 139 = 0 remainder 51 |
| 2 | 139 ÷ 51 = 2 remainder 37 |
| 3 | 51 ÷ 37 = 1 remainder 14 |
| 4 | 37 ÷ 14 = 2 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 15 | 1470 |
| 152 and 100 | 3800 |
| 159 and 51 | 2703 |
| 122 and 64 | 3904 |
| 86 and 112 | 4816 |