Least Common Multiple (LCM) of 100 and 72
The least common multiple (LCM) of 100 and 72 is 1800.
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 100 and 72?
First, calculate the GCD of 100 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 72 = 1 remainder 28 |
| 2 | 72 ÷ 28 = 2 remainder 16 |
| 3 | 28 ÷ 16 = 1 remainder 12 |
| 4 | 16 ÷ 12 = 1 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 132 | 14124 |
| 15 and 151 | 2265 |
| 51 and 161 | 8211 |
| 152 and 139 | 21128 |
| 187 and 106 | 19822 |