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Can two different pairs of numbers have the same LCM?

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Can two different pairs of numbers have the same LCM?

You just can’t guess the numbers if just LCM is given because a number can be the LCM for two different sets of numbers for e.g (2,15) and (6,5) both have LCM as 30. You need to have the HCF/GCD and LCM to exactly find the pair. Hope this helps.

Which pairs of numbers has a LCM of 24?

It is the least number among the common multiples. Since the least number among 24, 48 and 72 is “24”, the LCM of 8 and 6 is 24.

How many pairs of numbers exist such that HCF is 4 and LCM is 64?

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Answer: Two ordered pairs, or a single unordered pair, of the elements: 4, 64.

How many factors does 400 have?

As 400 is an even number, it will have 2 as its factor. Only composite numbers can have more than two factors. Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400.

What are two pairs of numbers whose LCM is the product of the numbers?

2 Answers By Expert Tutors When the LCM of two numbers equals the product of the two numbers, the two numbers have no common factors other than the number one. Counter example: 12 and 15, LCM=60 not 12*15 which equals 180 because 12 and 15 have a common factor of 3(the GCF) and if you divide 180 by 3 you get 60 !

What is the LCM of 48?

The LCM of 48 and 60 is 240. To find the least common multiple (LCM) of 48 and 60, we need to find the multiples of 48 and 60 (multiples of 48 = 48, 96, 144, 192 . . . .

What is the LCM of 54?

To find the LCM of 54 and 60 using prime factorization, we will find the prime factors, (54 = 2 × 3 × 3 × 3) and (60 = 2 × 2 × 3 × 5). LCM of 54 and 60 is the product of prime factors raised to their respective highest exponent among the numbers 54 and 60. ⇒ LCM of 54, 60 = 22 × 33 × 51 = 540.

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How do you find the possible pairs of LCM and HCF?

First, take the lcm and divide it by the hcf. Factor the number you got from that division into prime factors. To find the number of possible pairs, count the number of primes, ignoring multiplicity. For this example, there are 3 primes: 2, 3, and 5.

How many pairs are there in 36?

The factors of 36 in pairs are (1, 36), (4, 9), (6, 6), (12, 3), and (18, 2). There are a total of 5 pairs of factors of 36.

How do you find the LCM of more than 2 numbers?

Multiply the list of prime factors together to find the LCM. The LCM(a,b) is calculated by finding the prime factorization of both a and b. Use the same process for the LCM of more than 2 numbers. For example, for LCM(12,30) we find: Prime factorization of 12 = 2 × 2 × 3; Prime factorization of 30 = 2 × 3 × 5

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How many numbers have HCF of 5 and lcm of 100?

Since you want a pair of numbers whose LCM will be 400, you can choose 400 as one of them and the other a factor of 400 which happen to be 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 75, 80, 100, 200. Two natural numbers have HCF of 5 and LCM of 100. How many such pairs exist? Let two numbers be 5a & 5b where a & b are co-primes.

What is the LCM of P and Q?

So here we can say that as 400 (2^4*5^2) is the LCM of p and q, then p and q have only prime numbers 2 and 5. where a,b,x,y,i,j are non-negative integers. This is the main consideration of the whole problem.

How do you find the least common multiple of multiple multiples?

1 List the multiples of each number until at least one of the multiples appears on all lists. 2 Find the smallest number that is on all of the lists. 3 This number is the LCM Example: LCM (6,7,21)