Find the LCM of 306 and 657 & The Largest 5 Digit Number

To find the LCM of 306 and 657, we first find their prime factors:

• Prime factorization of 306: 2 × 3 × 3 × 17 = 2 × 3² × 17
• Prime factorization of 657: 3 × 3 × 73 = 3² × 73

To find the LCM, we multiply the highest powers of all prime factors involved: LCM = 2 × 3² × 17 × 73 LCM = 2 × 9 × 17 × 73 = 22,338

(Note: This is a classic NCERT Class 10 math problem where HCF is given as 9, and you can also use the formula: LCM × HCF = Product of two numbers. LCM = (306 × 657) / 9 = 22,338).

In the decimal number system, the largest single digit is 9. Therefore, to create the largest possible number with 5 digits, you simply write the digit 9 five times.

• The Largest 5-Digit Number is 99,999 (Ninety-nine thousand, nine hundred and ninety-nine).
• If you add just 1 to this number, it becomes 100,000, which is the smallest 6-digit number.