Least Common Multiple (LCM) of 72 and 52
The least common multiple (LCM) of 72 and 52 is 936.
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 72 and 52?
First, calculate the GCD of 72 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 52 = 1 remainder 20 |
| 2 | 52 ÷ 20 = 2 remainder 12 |
| 3 | 20 ÷ 12 = 1 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 138 | 15042 |
| 42 and 87 | 1218 |
| 184 and 102 | 9384 |
| 11 and 146 | 1606 |
| 102 and 91 | 9282 |