Least Common Multiple (LCM) of 75 and 53
The least common multiple (LCM) of 75 and 53 is 3975.
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 53?
First, calculate the GCD of 75 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 53 = 1 remainder 22 |
| 2 | 53 ÷ 22 = 2 remainder 9 |
| 3 | 22 ÷ 9 = 2 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 164 | 17548 |
| 111 and 91 | 10101 |
| 153 and 70 | 10710 |
| 169 and 139 | 23491 |
| 183 and 98 | 17934 |