how do find lcm and gcf of 165,275
Here is one of the most common methods
165 = 3x5x11
275 = 5x5x11
The gcf is the largest numbers that appears in both
which is 5x11 or 55
the lcm is the string of factors which appear in one or the other
which is 3x5x5x11 =
To find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of two numbers, 165 and 275, we can follow these steps:
Step 1: Prime Factorization
Find the prime factorization of both numbers.
1. Prime factorization of 165:
165 = 3 × 5 × 11
2. Prime factorization of 275:
275 = 5 × 5 × 11
Step 2: Find LCM
The LCM is found by multiplying the highest powers of all the common and non-common prime factors.
The common prime factors are 5 and 11. The highest power of 5 is 5^2, and the highest power of 11 is 11^1.
LCM = 5^2 × 11^1 = 25 × 11 = 275
Therefore, the LCM of 165 and 275 is 275.
Step 3: Find GCF
The GCF is found by multiplying the common prime factors with the smallest exponent.
The common prime factors are 5 and 11. The smallest exponent for 5 is 5^1, and the smallest exponent for 11 is 11^1.
GCF = 5^1 × 11^1 = 5 × 11 = 55
Therefore, the GCF of 165 and 275 is 55.
In summary:
LCM = 275
GCF = 55
To find the LCM (Least Common Multiple) and GCF (Greatest Common Factor) of the numbers 165 and 275, you need to follow these steps:
To find the GCF:
1. List all the factors of each number.
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, and 165.
The factors of 275 are 1, 5, 11, 25, 55, 137, and 275.
2. Identify the common factors of both numbers.
The common factors of both 165 and 275 are 1, 5, and 55.
3. Find the greatest common factor.
The largest common factor among 1, 5, and 55 is 55. Therefore, the GCF of 165 and 275 is 55.
To find the LCM:
1. List the multiples of each number until you find a common multiple.
The multiples of 165 are 165, 330, 495, 660, and so on.
The multiples of 275 are 275, 550, 825, 1100, and so on.
2. Identify the common multiples of both numbers.
As you can see, the first common multiple of both 165 and 275 is 825.
3. Determine the least common multiple.
Therefore, the LCM of 165 and 275 is 825.
So, the GCF of 165 and 275 is 55, and the LCM is 825.