The LCM of 148 and 185 is _____.

Given:

Two numbers: 148 and 185

Calculation:

Let's use the prime factorization method.

148 = 2 × 2 × 37

185 = 5 × 37

3. Calculate the LCM:

The highest power of all prime factors that appear in either factorization.

Prime factors are 2, 5, and 37.

Highest power of 2 is 2².

Highest power of 5 is 5¹.

Highest power of 37 is 37¹.

LCM(148, 185) = 2² × 5 × 37

= 4 × 5 × 37

= 20 × 37

= 740

∴ The correct answer is option (3).

Alternate MethodFormula used:

LCM × HCF = Product of the numbers

Calculation:

HCF of 148 and 185 = 37

Product of the numbers = 148 × 185 = 27380

⇒ LCM = \(\dfrac{\text{Product of the numbers}}{\text{HCF}}\)

⇒ LCM = \(\dfrac{27380}{37}\)

⇒ LCM = 740