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To find the HCF and LCM of two (or more) numbers list the numbers in their prime factorisations in power format; then:
- HCF = product of the primes to the LOWEST power across all the numbers;
- LCM = product of the primes to the HIGHEST power across all the numbers.
The HIGHEST power of a prime must be at least the LOWEST power of a prime.
Thus if a prime appears in the HCF of the numbers (with a power greater than or equal to 1) it MUST also appear in the LCM of the numbers.
If the HCF of some numbers is 15, then: 15 = 3 × 5 which means that the primes 3 and 5 MUST both apear in the LCM.
But 175 = 5² × 7, which does NOT include 3, so 175 CANNOT be the LCM of some numbers which have a HCF of 15.
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Which 2 nos have same LCM and HCF?
Any two of the same number. The GCF and LCM of 10 and 10 is 10.
Does the HCF of any two no is always a factor of their LCM?
If two numbers are expressed as ab and cb this is easier to work out. Assume that a and c have no common prime factors. Thus, the HCF of the two numbers will be b. The LCM is the two numbers multiplied by each other, divided by the HCF. So the LCM will be abc. b is a factor of abc, and so the HCF will always be a factor of their LCM.
What is the HCF and LCM of 36 and 75?
To find the HCF you first have to write the numbers as their prime factors: 36 = 2x2x3x3 75 = 3x5x5 The next step is to identify any common prime factors. In this case both numbers have 3 as a prime factor. Thus the HCF is 3. To find the LCM you need to multiply the numbers together and divide by the HCF. 36x75/3 = 900 Thus the LCM of 36 and 75 is 900.
What is the HCF and LCM of 63 and 21?
First you need to break the numbers into their prime factors. In this case we get: 63 = 3x3x7 21 = 3x7 The next step is to identify any common prime factors. In this case both have a 3 and a 7 as prime factors. Multiply these together and you get 3x7 = 21. This is the HCF. To find the LCM you just multiply the numbers together and divide by the HCF. 63x21/21 = 63 Thus 63 is the LCM.
What is HCF and LCM of 30 and 45?
To find the HCF you first need to break the numbers down into their prime factors. In this case we have: 30 = 2x3x5 45 = 3x3x5 The next step is to identify any common factors. In this case both numbers have 3 and 5 as prime factors. To find the HCF, multiply these together: 3x5 = 15. To get the LCM, multiply the numbers together then divide by the HCF: 30x45/15 = 90.
Which 2 nos have same LCM and HCF?
Any two of the same number. The GCF and LCM of 10 and 10 is 10.
Does the HCF of any two no is always a factor of their LCM?
If two numbers are expressed as ab and cb this is easier to work out. Assume that a and c have no common prime factors. Thus, the HCF of the two numbers will be b. The LCM is the two numbers multiplied by each other, divided by the HCF. So the LCM will be abc. b is a factor of abc, and so the HCF will always be a factor of their LCM.
HCF and LCM of p and p plus 1?
To consecutive numbers cannot have any common prime factors. Thus the HCF of p and (p+1) will be 1. To find the LCM, you multiply two numbers together and divide by the HCF. In this case, you'd do p(p+1)/1 This simplifies to p2+p So the HCF is 1 and the LCM is p2+p
What job would you have to use LCM and HCF for?
Any job where you need to add or subtract fractions.
What is the HCF and LCM of 36 and 75?
To find the HCF you first have to write the numbers as their prime factors: 36 = 2x2x3x3 75 = 3x5x5 The next step is to identify any common prime factors. In this case both numbers have 3 as a prime factor. Thus the HCF is 3. To find the LCM you need to multiply the numbers together and divide by the HCF. 36x75/3 = 900 Thus the LCM of 36 and 75 is 900.
What is the difference between the LCM and HCM of 42 nd 84?
Whenever one of the numbers is a multiple of the other, the larger number is the LCM and the smaller number is the GCF. In this case, the difference between them is 42. The highest common multiple of any set of integers is infinite.
What is the HCF of 0.6 0.36 0.24?
The concept of HCF is normally not applied to fractions. This is because once you introduce fractions, any number is divisible by any other number.
What is the HCF and LCM of 36 and 60?
To do this you first need to express each number as a product of their prime factors: 36 = 2x2x3x3 60 = 2x2x3x5 The next step is to identify any common prime factors. In this case, both numbers have a 2 a 2 and a 3 as prime factors. Multiply these together and you get 12. Therefore the HCF of 36 and 60 is 12. To find the LCM, multiply the numbers together and divide by the hcf: 36x60/12 = 180 So 180 is the LCM of 36 and 60.
What is the the LCM of 2 and any odd number?
The LCM of 2 and any odd number is their product.
What is the HCF and LCM of 63 and 21?
First you need to break the numbers into their prime factors. In this case we get: 63 = 3x3x7 21 = 3x7 The next step is to identify any common prime factors. In this case both have a 3 and a 7 as prime factors. Multiply these together and you get 3x7 = 21. This is the HCF. To find the LCM you just multiply the numbers together and divide by the HCF. 63x21/21 = 63 Thus 63 is the LCM.
What is HCF and LCM of 30 and 45?
To find the HCF you first need to break the numbers down into their prime factors. In this case we have: 30 = 2x3x5 45 = 3x3x5 The next step is to identify any common factors. In this case both numbers have 3 and 5 as prime factors. To find the HCF, multiply these together: 3x5 = 15. To get the LCM, multiply the numbers together then divide by the HCF: 30x45/15 = 90.
What can 175 be multiplied by?
Any number
