what is the GCF and LCM of 36 and 84
The GCF for them is 3 and 2. and the LCF is 7
The GCF is 7. The LCM is 252.
To find the GCF (Greatest Common Factor) and LCM (Least Common Multiple) of two numbers, such as 36 and 84, we can use a step-by-step process.
Step 1: Determine the prime factors of both numbers.
To find the prime factors of 36, we divide it by prime numbers starting from 2 until we cannot divide any further.
36 ÷ 2 = 18
18 ÷ 2 = 9
So, the prime factors of 36 are 2 × 2 × 3 = 2² × 3.
Similarly, for 84:
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
Hence, the prime factors of 84 are 2 × 2 × 3 × 7 = 2² × 3 × 7.
Step 2: Find the GCF.
To find the GCF, we take the common prime factors of both numbers and multiply them.
Common prime factors of 36 and 84:
2² × 3
Therefore, the GCF of 36 and 84 is 2² × 3 = 12.
Step 3: Find the LCM.
To find the LCM, we take the highest power of each prime factor that appears in either number and multiply them.
Prime factors of 36: 2² × 3
Prime factors of 84: 2² × 3 × 7
To find the LCM, we take the highest power of each factor:
2² × 3 × 7
Hence, the LCM of 36 and 84 is 2² × 3 × 7 = 252.
Therefore, the GCF of 36 and 84 is 12, and the LCM is 252.