Least Common Multiple (LCM) of 119 and 72
The least common multiple (LCM) of 119 and 72 is 8568.
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 119 and 72?
First, calculate the GCD of 119 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 72 = 1 remainder 47 |
| 2 | 72 ÷ 47 = 1 remainder 25 |
| 3 | 47 ÷ 25 = 1 remainder 22 |
| 4 | 25 ÷ 22 = 1 remainder 3 |
| 5 | 22 ÷ 3 = 7 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 101 | 9090 |
| 70 and 73 | 5110 |
| 68 and 170 | 340 |
| 18 and 140 | 1260 |
| 80 and 131 | 10480 |