Practice Questions
Find the LCM of 84 and 126 using prime factorisation.
$84 = 2^2 \times 3 \times 7$; $126 = 2 \times 3^2 \times 7$. $\text{LCM} = 2^2 \times 3^2 \times 7 = 4 \times 9 \times 7 = 252$.
Find the LCM of $(2^3 \times 3^2)$ and $(2^2 \times 3^4)$.
Take the highest powers of each prime: $2^3$ and $3^4$. $\text{LCM} = 8 \times 81 = 648$.
Find the least number divisible by 15, 20 and 30.
$\text{LCM}(15, 20, 30)$ is the smallest number that is a multiple of all three. 60 is the first such number.
Find the smallest number which when divided by 8, 10 and 12 leaves remainder 5.
$\text{LCM}(8, 10, 12) = 120$. Smallest number = $120 + 5 = 125$.
Two traffic lights change every 24 seconds and 36 seconds respectively. When will they change together again?
They will change together at intervals equal to the $\text{LCM}(24, 36) = 72$ seconds.
Find the LCM of $3/4, 5/6$ and $7/8$.
$\text{LCM} = \text{LCM}(3, 5, 7) / \text{HCF}(4, 6, 8) = 105 / 2$.
Find the least 4-digit number divisible by 18 and 24.
$\text{LCM}(18, 24) = 72$. Least 4-digit number is 1000. $1000 / 72 \approx 13.88$. Next integer is 14. $14 \times 72 = 1008$.
Three bells ring at intervals of 20, 30 and 40 minutes. When will they ring together again?
$\text{LCM}(20, 30, 40) = 120$ minutes, which is 2 hours.
Find the least number which when divided by 6, 9 and 15 leaves remainder 4 in each case.
$\text{LCM}(6, 9, 15) = 90$. Required number = $90 + 4 = 94$.
Find the LCM of 0.36, 0.48 and 0.72.
Write as fractions: $36/100, 48/100, 72/100 = 9/25, 12/25, 18/25$. $\text{LCM} = \text{LCM}(9,12,18)/\text{HCF}(25,25,25) = 36/25 = 1.44$.
Premium Content
Unlock LCM Quiz and all premium lessons with a subscription.
From ₹199.99/year — See plans