Important shortcut formula on hcf and lcm:
1. Hcf of numbers*Lcm of numbers=Product of numbers
2. To find the greatest number that will divide x,y and z :
Hcf of x,y,z.
3. The greatest number that will divide x,y,z leaving same remainders in each case will be hcf of |(x-y)|,|(y-z)|,|(z-x)|
4.The greatest number that will divide x,y,z leaving remainders a,b,c will be hcf of (x-a),(y-b),(z-c)
5. The least number that is exactly divisible by x,y,z will be lcm of x,y,z.
6. The least number which when divided by x,y,z leaves the same remainder r in each case will equal to (LCM of x,y,z)+r.
7. The least number which when divided by x,y,z leaves remainders a,b,c such that (x-a)=(y-b)=(z-c)=k
will be equal to (LCM of x,y,z)-k.
8. Remember ,Hcf is smaller than the numbers and is a common factor of the numbers. Lcm is greater than the numbers and is divisible by the given numbers.
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1. Hcf of numbers*Lcm of numbers=Product of numbers
2. To find the greatest number that will divide x,y and z :
Hcf of x,y,z.
3. The greatest number that will divide x,y,z leaving same remainders in each case will be hcf of |(x-y)|,|(y-z)|,|(z-x)|
4.The greatest number that will divide x,y,z leaving remainders a,b,c will be hcf of (x-a),(y-b),(z-c)
5. The least number that is exactly divisible by x,y,z will be lcm of x,y,z.
6. The least number which when divided by x,y,z leaves the same remainder r in each case will equal to (LCM of x,y,z)+r.
7. The least number which when divided by x,y,z leaves remainders a,b,c such that (x-a)=(y-b)=(z-c)=k
will be equal to (LCM of x,y,z)-k.
8. Remember ,Hcf is smaller than the numbers and is a common factor of the numbers. Lcm is greater than the numbers and is divisible by the given numbers.
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