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Q: How big can the LCM be for any pair of natural numbers?

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The LCM can be any positive integer.

Which pair of numbers has an LCM of 40?

Pick any two numbers. All pairs of numbers have an LCM.

The LCM must be the other number in the pair. For any pair of numbers X and Y, X*Y = GCF*LCM and the result follows if you put GCF = X (or Y).

Any pair of prime numbers. 5 and 7 11 and 13

That pair of numbers doesn't exist, as the least common factor of any pair of positive numbers is 1. The LCM of 3 and 6 is 6. The GCF of 6 and 12 is 6.

For this you will need a couple of helper algorithms. The first is the GCD (greatest common divisor) which is expressed as follows:procedure GCD (a, b) isinput: natural numbers a and bwhile ab doif a>blet a be a-belselet b be b-aend ifend whilereturn aThe second algorithm is the LCM (least common multiple) of two numbers:procedure LCM (a, b) isinput: natural numbers a and b return (a*b) / GCD (a, b)Now that you can calculate the GCD and LCM of any two natural numbers, you can calculate the LCM of any three natural numbers as follows:procedure LCM3 (a, b, c) isinput: natural numbers a, b and c return LCM (LCM (a, b), c)Note that the LCM of three numbers first calculates the LCM of two of those numbers (a and b) and then calculates the LCM of that result along with the third number (c). That is, if the three numbers were 8, 9 and 21, the LCM of 8 and 9 is 72 and the LCM of 72 and 21 is 504. Thus the LCM of 8, 9 and 21 is 504.

35 and 36 are coprime (any pair of consecutive numbers must be). So lcm(35, 36) = 35*36 = 1260.

Because prime numbers don't have any common prime factors. Their GCF is 1. Since the product of the GCF and LCM of a pair of numbers equals the product of the numbers, the LCM has to be equal to the product.

The LCM is not defined for any set of numbers that contains a zero.

Absolutely !.. Any prime number only has itself and 1 as its factors.

The LCM of any three distinct prime numbers is their product.

The LCM of two numbers will never be less than the GCF.

The LCM of any two consecutive numbers greater than zero is the two numbers multiplied together. eg. the LCM of 10 and 11 is: 10*11=110

For any two natural numbers a & b: Their LCM is b if b is the multiple of a. Here, 135 is the multiple of 27(27 x 5 = 135). Therefore, LCM of 27 & 135 = 135.

Any pair of prime numbers as for example 19 and 23

Their product.

In any number pair where one of the numbers is a multiple of the other, that number is the LCM.

No. You can only find the LCM of at least two numbers, prime or otherwise. The LCM of any two prime numbers is their product.

It is not at all clear how a leaf has any bearing on the value of the LCM.

Any two that are relatively prime.

Any pair of numbers, whole or fractional (or even irrational) are proportional.Any pair of numbers, whole or fractional (or even irrational) are proportional.Any pair of numbers, whole or fractional (or even irrational) are proportional.Any pair of numbers, whole or fractional (or even irrational) are proportional.

Any pair of prime numbers

The LCM of 3, 15 and 36 is 180.

Yes.