Cracking LCM & HCF Remainder Problems: 8 Simple Formulas Explained

Описание: Mayank explains the following 8 formulas to easily solve all HCF and LCM problems involving remainders

For HCF Remainder Problems:
1. Greatest number which divides x, y and z = HCF (x, y, z)
2. Greatest number which divides x, y and z and leaves remainder r = HCF(x - r, y - r, z - r)
3. Greatest number which divides x, y and z and leaves same remainder = HCF(|x - y|, |y - z|, |z - x|)
4. Greatest number which divides x, y and z and leaves remainder a, b, c = HCF(x - a, y - b, z - c)

For LCM Remainder Problems:
1. Smallest number divisible by x, y and z = LCM(x, y, z)
2. Smallest number of n digits divisible by x, y and z = Multiple of LCM(x, y, z)
3. Smallest number when divided by x, y and z leaves same remainder r = LCM(x, y, z) + r
4. Smallest number when divided by x, y and z leaves remainder a, b, c where x - a = y - b = z - c = common difference d is LCM (a, b, c) - d

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Recap @0:20
Method @0:23
Problem Keywords @0:31
HCF Remainder Problems 4 Types @0:56
Greatest Number Which Divides x, y and z? HCF Types 1 (Simple) @1:16
Greatest Number Which Divides x, y and z Leaves same remainder r (Given)? HCF Type 2 (Same Remainder - Given) @2:02
Greatest Number Which Divides x, y and z Leaves same remainder r (Not Given)? HCF Type 3 (Same Remainder – Not Given) @4:20
Greatest Number Which Divides x, y and z Leaving Remainder a, b and c (Respectively)? HCF Type 4 (Different Remainder - Given) @8:36
HCF Problems -4 Types Summary Understand and Remember @10:36
LCM Remainder Problems 4 Types @13:24
Smallest Number Divisible by x, y, and z? LCM Type 1 (Simple) @13:36
Smallest/Largest Number of n Digits Divisible by x, y, z? LCM Type 2 (Multiples of LCM) @15:14
Smallest Number when Divided by x, y and z Leaves same remainder r (Given)? LCM Type 3 (same Remainder) @22:14
Smallest Number when Divided by x, y and z Leaves remainder a, b, c? LCM Type 4 (Different Remainder) @25:20
LCM Problems -4 Types Summary Understand and Remember @32:18
Variations of LCM (Understand) @34:11
Example – 1 @35:59
Example –2 @40:59
Example – 3 (Advanced) @42:44
Generalization – Chinese Remainder Theorem @47:20
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