Question

LOM of is, 20, 25, 45,15​

Answer 1

Prime factorisation of:-

20 = 2² × 5¹

25 = 5²

45 = 3² × 5¹

15 = 3¹ × 5¹

Now, LCM = Product of the highest powers present in the prime Factorisation of the given numbers.

∴ LCM(20, 25, 45, 15) = 2² × 3² × 5² = 4 × 9 × 5 = 45 × 4 = 180.

More:-

• Only the rational numbers where the denominator is in the form of 2^a × 5^b only terminates.
• Number of places after with the given rational number where the denominator is in the form of 2^a × 5^b is given by max(a, b).
• HCF(x, y) × LCM(x, y) = xy.
• LCM(x, y, z) = [x × y × z × HCF(x, y, z)]/[HCF(x, y) × HCF(y, z) × HCF(x, z)].
• HCF(x, y, z) = [x × y × z × LCM(x, y, z)]/[LCM(x ,y) × LCM(y, z) × LCM(x, z)].
• HCF of fractions = (HCF of Numerators)/(LCM of denominators).
• LCM of fractions = (LCM of numerators)/(HCF of denominators).