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lcm and hcf


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If a and b are two natural numbers
then HCF[a,b]*LCM[a,b]= a * b

If the HCF of two numbers is 11 and their
LCM is 7700, and one of the numbers is 275
find the other number

Let the other number be x
HCF[a,b]*LCM[a,b]= a * b
therefore
11*7700 = 275 * x
x = 11*7700 /275=308
other number is 308
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HCF of fractions = [HCF of numerator]/[LCM of denominators ]

LCM of fractions = [LCM of numerator]/[HCF of denominators ]

largest number that can exactly divide [a,b,c]=HCF[a,b,c]


least number that exactly divisible by [a,b,c]=LCM[a,b,c]

largest number that can  divide [a,b,c] leaving remainder k for each =HCF[(a-k),(b-k),(c-k)]

largest number that can  divide [a,b,c] leaving same remainder  for each =HCF[(b-a),(c-b),(c-a)]
if a<b<c

least number that when divided by each of [a,b,c] leaves a remainder k=LCM[a,b,c]+k
 


other questions and problems:

*integral calculus integration formula





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