Q: Can the HCF of two numbers be a factor of their LCM?

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If the HCF (Highest Common Factor) of two numbers is 1, then the two numbers are relatively prime and their LCM is the product of the two numbers.

HCF of 17 and 68 is 17 ..( Lowest Prime factor ) LCM Of 102 and 476 is 7*2^2*3*17 which is 1428 .. ==> Sum of HCF and LCM are 1428+17= 1445 .

HCF of 20 means the two numbers have common prime factors of 2, 2 and 5. However, LCM of 535 means that both of the numbers are odd. This cannot be the case if they have a prime factor of 2. Thus two numbers cannot have 20 as hcf and 535 as lcm.

5 and 10 lcm- 10 and hcf= 5

Two or more numbers are needed to solve for HCF or LCM.

Related questions

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 means the highest common factor of two or more numbers. LCM means the lowest common multiple of two or more numbers.

If the HCF (Highest Common Factor) of two numbers is 1, then the two numbers are relatively prime and their LCM is the product of the two numbers.

HCF of 17 and 68 is 17 ..( Lowest Prime factor ) LCM Of 102 and 476 is 7*2^2*3*17 which is 1428 .. ==> Sum of HCF and LCM are 1428+17= 1445 .

The product of the GCF and the LCM of two numbers is equal to the product of the original two numbers. Multiply the GCF and the LCM. The original two numbers will be another factor pair of that total. Find the factor pair that has that GCF and LCM.

HCF of 20 means the two numbers have common prime factors of 2, 2 and 5. However, LCM of 535 means that both of the numbers are odd. This cannot be the case if they have a prime factor of 2. Thus two numbers cannot have 20 as hcf and 535 as lcm.

No. The LCM MUST be a multiple of the HCF.

No, 2 and 10 are factors of 20. The LCM of 2 and 10 is 10.

The LCM of two numbers is twice their HCF. This means that the two numbers are opposite of each other in terms of their largest common factor (LCF). Additionally, because the LCF is 2, you can say that these two numbers are opposite integers.

5 and 10 lcm- 10 and hcf= 5

Two or more numbers are needed to solve for HCF or LCM.

You cannot. The numbers 2 and 12 have hcf = 2 and LCM = 12 The numbers 4 and 6 also have hcf = 2 and LCM = 12 So if you just knew the hcf and LCM you would not know which of the two was the required pair.