Can two different pairs of numbers have the same least common multiple? Yes. 15 and 4, and 12 and 5, for example. In general, if a, b, and c are all relatively prime (in particular if they’re all prime) then the LCM of ab and c is the LCM of a and bc is the LCM of AC and b, and all are equal to abc.
What are the two types of LCM?
The least common multiple of two numbers is the “smallest non-zero common number” which is a multiple of both the numbers.
- The different methods to find least common multiple of two or more numbers are:
- LCM using prime factorization.
- Figure: Prime factorization trees for the number 36 and 48.
- LCM using repeated division.
What is the LCM of two different numbers?
The LCM of two different numbers is 18, and the GCF is 6. What are the numbers? They must have the prime factors 2×3 = 6 in common. 18 = 2×3×3 and 6 = 2×3 would do. The numbers themselves are 6 and 18. If the LCM of the two numbers is 18, that means both numbers have to be factors of 18. So each number could be 1, 2, 3, 6, 9, or 18.
What does the LCM of 6 and 18 mean?
18 = 2×3×3 and 6 = 2×3 would do. The numbers themselves are 6 and 18. If the LCM of the two numbers is 18, that means both numbers have to be factors of 18. So each number could be 1, 2, 3, 6, 9, or 18. If the GCF of the two numbers is 6, that means both numbers are divisible by 6. So each number could be 6, 12, 18, 24, etc.
How many pairs are possible if the LCM is 210?
Total 4 pairs possible…. There are only 4 pairs totally possible if the lcm of two numbers is 210 and their hcf is14 . Still have questions? what is this •.•?? is it because ??
Is the product of two numbers equal to the GCF?
In general, you may also be able to use the fact that the product of any two numbers will equal the product of (their lcm)×(their gcf). Let’s show why with an example pair: 6 and 15. GCF: They both have just a 3 in common, so their GCF is 3. LCM: The first number that’s a multiple of both will need to be a multiple of 2, 3, and 5.
