Least Common Multiple (LCM) of 75 and 139
The least common multiple (LCM) of 75 and 139 is 10425.
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 75 and 139?
First, calculate the GCD of 75 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 139 = 0 remainder 75 |
| 2 | 139 ÷ 75 = 1 remainder 64 |
| 3 | 75 ÷ 64 = 1 remainder 11 |
| 4 | 64 ÷ 11 = 5 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 162 | 18630 |
| 35 and 128 | 4480 |
| 132 and 97 | 12804 |
| 62 and 176 | 5456 |
| 62 and 76 | 2356 |