The LCF is: 1
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The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. The greatest common factor of 4 and 8 is 8. (See related question "What is the greatest common factor of 4 and 8?" for this calculation.) So, the least common multiple is 4 x 8 ÷ 4 = 8. Common multiples of 4 and 8 include 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, etc. Although 16 is a common multiple, it is not the least common multiple.
The numbers 16 and 27 don't have any common prime factors. 16 = 2 x 2 x 2 x 2 27 = 3 x 3 x 3 Therefore, the numbers are relatively prime and their greatest common factor is 1. Another way to approach this is to look at the difference between 16 and 27, which is 11. The greatest common factor of two numbers cannot be larger than the difference between the two numbers. The greatest common factor of two numbers must also be a factor of the difference between the numbers. The difference, 11, is a prime number, so the greatest common factor must be either 11 or 1. Since the numbers are not evenly divisible by 11, so the greatest common factor is 1.
The greatest common factor is the highest number that divides exactly into two or more numbers. 16: 1, 2, 4, 8, 16 40: 1, 2, 4, 5, 8, 10, 20, 40 72: 1, 2, 3, 4, 6,8, 9, 12, 18, 24, 36, 72 The greatest common factor of 16, 40 and 72 is 8.
112 = 16 x 7 and 96 = 32 x 3, or 16 x 6. I grouped it like this to show the common factor of 16. So the LCM is the common factor (once) times the other factors.16 x 7 x 6 = 672.
The GCF is 8.