Least Common Multiple (LCM) of 75 and 156
The least common multiple (LCM) of 75 and 156 is 3900.
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 156?
First, calculate the GCD of 75 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 156 = 0 remainder 75 |
| 2 | 156 ÷ 75 = 2 remainder 6 |
| 3 | 75 ÷ 6 = 12 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 45 | 135 |
| 64 and 116 | 1856 |
| 69 and 103 | 7107 |
| 123 and 138 | 5658 |
| 44 and 141 | 6204 |