How do I figure out the GCF and the LCM of these three numbers 10-55 and 45
I pasted below an example that reiny (tutor here) did recently.
10 and 55 are done in this example. Follow what reiny did for 45.
EXAMPLE
10 = 2*5
75 = 3*5*5
55 = 5*11
The GCF is the largest number that divides into all three numbers,
in this case 5
the GCF ≤ the smallest of the numbers
The LCM is that number which contains all the factors that are found in all the numbers
in this case it is 2*3*5*5*11 = 1650
It is the smallest number that the given numbers divide INTO evenly
the LCD ≥ the largest of the given numbers.
for the LCD I usually write down the longest string of factors, then looking at the other group of factors, I include any others not yet included in my string.
I am looking for the GCF and LCM of the ages 50,55,10. Can you help me with that?
To find the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) of three numbers, such as 10, 55, and 45, you can follow these steps:
1. Prime factorization: First, express each number as a product of its prime factors.
- For 10, the prime factorization is 2 * 5.
- For 55, the prime factorization is 5 * 11.
- For 45, the prime factorization is 3 * 3 * 5.
2. GCF: To find the GCF, identify the common prime factors and multiply them.
- The common prime factors among the three numbers are 5.
- Therefore, GCF = 5.
3. LCM: To find the LCM, multiply all the unique prime factors with the highest exponent.
- The unique prime factors and their highest exponents are 2^1, 3^2, and 11^1.
- Therefore, LCM = 2 * 3^2 * 5 * 11 = 330.
Thus, the GCF of 10, 55, and 45 is 5, and the LCM is 330.