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How do you Find a pair of numbers whose LCM is 75 and whose GCF is 5?
75 = 3*5*5, so the first pair that comes to mind is 3*5 and 5*5.LCM(15, 25) = 75.And it conveniently happens to be that GCD*(15, 25) = 5.So {15, 25} is the answer (at least an answer).*GCD is "Greatest Common Divisor" and a more official way of saying GCF.* * * * *Yes, it is an answer.Consider LCM/GCF = 75/5 = 15If p and q are any two coprime factors of LCM/GCF = 15, then p*GCF and q*GCF will be an answer.The above answer used p = 3 and q = 5.The other possible pair is p = 1 and q = 15 which gives the pair as 5 and 75.
What is the gcf of 9 and 24 and 36?
The GCF is 3.
What is the least common multiple of 3 and 12?
The least common multiple (LCM) of 3 and 12 is 12. Because 12 is a factor of 3, it is automatically the LCM of the set.You can also find the LCM by listing the multiples of each number in the set, and finding the lowest one in each list.The multiples of 3 are 3, 6, 9, 12, and so on.The multiples of 12 are 12, 24, and so on.So the LCM is 12.Another method is dividing the product of the pair of numbers by their GCF.The product of 3 and 12 is 36.The GCF of 3 and 12 is 3. (Since 3 is a factor of 12, it is automatically the GCF of the set).So the LCM is 36/3 = 12.The least common multiple is the smallest number that all the numbers are a factor of. In this case it's 12. This is because 12x1=12 and 3x4=12.The LCM is 12.
How do you find a pair of numbers when the GCF is given?
To find a pair of numbers with a given GCF, take the GCF number and double it. The pair of numbers is the GCF, and two times the GCF. For instance, two numbers with a GCF of 3 are 3 and 6.
Why is the product of the LCM and HCF the same as the product of the original pair of numbers?
It's the way numbers work. Consider 32 and 33. Consecutive integers are relatively prime, that is, their GCF is 1. If two numbers have a GCF of 1, the LCM will be their product. 32 x 33 = 1056 1 (GCF) x 1056 (LCM) = 1056 2 x 528 = 1056 3 x 352 = 1056 4 x 264 = 1056 Notice the pattern. As the GCF increases, the LCM decreases. Consider 32 and 34. Consecutive even numbers have a GCF of 2. The LCM of 32 and 34 is 544. 32 x 34 = 1088 2 (GCF) x 544 (LCM) = 1088 If you know either the GCF or the LCM of two numbers, you can find the other one without factoring again. The GCF of 28 and 36 is 4. Their product is 1008. Their LCM is 1008 divided by 4, or 252.
