The LCM of 9 and itself is 9 — since any number is a multiple of itself, and there’s no smaller positive integer that both 9 and 9 share as a multiple.
What is the LCM for 9 and 9?
The LCM of 9 and 9 is 9 because when both numbers are identical, their least common multiple is simply the number itself.
Same logic applies to any repeated pair, like 5 and 5, which also have an LCM of 5. It’s the smallest positive integer both numbers divide into without leaving a remainder.
How do you find the LCM of Class 9?
To find the LCM for Class 9 math, use prime factorization or the division method — both are standard approaches in most Class 9 curricula.
First, write each number as a product of its prime factors. Then take the highest power of each prime present and multiply them together. For example, to find the LCM of 12 and 18: 12 = 2² × 3, 18 = 2 × 3² → LCM = 2² × 3² = 36. You can also use the formula LCM(a, b) = (a × b) / GCD(a, b), which works great for larger numbers.
What is the LCM of 9 and 6 and 9?
The LCM of 6, 9, and 9 is 18 — since 18 is the smallest number divisible by 6, 9, and 9.
When you see a repeated number, it doesn’t change the LCM at all. Just treat the set as {6, 9}, and find the LCM of those two. Multiples of 6: 6, 12, 18, 24… Multiples of 9: 9, 18, 27… The smallest common multiple is clearly 18.
What is the LCM 9 and 12?
The LCM of 9 and 12 is 36 — the smallest number both 9 and 12 divide into evenly.
You can find this by listing multiples: 9 → 9, 18, 27, 36, 45… 12 → 12, 24, 36, 48… The first common one is 36. Or use the formula: LCM(9,12) = (9 × 12) / GCD(9,12) = 108 / 3 = 36. Honestly, this is one of the cleaner LCM calculations.
What is the LCM for 15 and 9?
The LCM of 15 and 9 is 45 — the smallest positive integer divisible by both 15 and 9.
Break it down: 15 = 3 × 5, 9 = 3² → LCM = 3² × 5 = 45. Or list multiples: 15 → 15, 30, 45, 60… 9 → 9, 18, 27, 36, 45… The first overlap is 45. Not too shabby, right?
What is the GCF of 55 and 77?
The GCF of 55 and 77 is 11 — the largest number that divides both evenly.
Prime factors: 55 = 5 × 11, 77 = 7 × 11. The only common prime factor is 11, so the GCF is 11. You can also use the Euclidean algorithm: 77 ÷ 55 = 1 remainder 22; 55 ÷ 22 = 2 remainder 11; 22 ÷ 11 = 2 remainder 0 → GCF = 11. This method never fails.
What is LCM example?
An LCM is the smallest integer that is a multiple of two or more numbers — like the LCM of 4 and 6 is 12, because 12 is the smallest number both 4 and 6 divide into.
Another example: LCM of 5 and 7 is 35, since 35 is the first number both 5 and 7 fit into. LCM is useful in real life for timing events, like when two buses with different schedules will arrive at the same time. Imagine two buses: one comes every 15 minutes, the other every 20 minutes. Their LCM is 60, so they’ll sync up every hour.
What is the LCM formula?
The LCM formula for two numbers a and b is LCM(a, b) = (a × b) / GCD(a, b), where GCD is the greatest common divisor.
For example, LCM(8, 12) = (8 × 12) / 4 = 96 / 4 = 24. This formula works because multiplying the numbers gives a shared multiple, and dividing by their GCD removes the overlap, leaving the least common multiple. It’s a neat little trick that saves time.
What is the LCM 4 and 9?
The LCM of 4 and 9 is 36 — the smallest number both 4 and 9 divide into without a remainder.
Prime factors: 4 = 2², 9 = 3² → LCM = 2² × 3² = 36. Or list multiples: 4 → 4, 8, 12, 16, 20, 24, 28, 32, 36… 9 → 9, 18, 27, 36… First match is 36. No surprises here.
What is the LCM of 8 and 9?
The LCM of 8 and 9 is 72 — since 72 is the first number both 8 and 9 divide into evenly.
8 and 9 are coprime (no common factors other than 1), so their LCM is simply their product: 8 × 9 = 72. This is a quick trick when two numbers share no prime factors — just multiply them. Works every time.
What is the LCM of 8 and 10?
The LCM of 8 and 10 is 40 — the smallest number both 8 and 10 divide into without leaving a remainder.
Prime factors: 8 = 2³, 10 = 2 × 5 → LCM = 2³ × 5 = 40. Or list multiples: 8 → 8, 16, 24, 32, 40… 10 → 10, 20, 30, 40… First overlap is 40. Simple enough.
What is the LCM for 6 7 and 9?
The LCM of 6, 7, and 9 is 126 — the smallest number divisible by all three.
Prime factors: 6 = 2 × 3, 7 = 7, 9 = 3² → LCM = 2 × 3² × 7 = 126. You can also find LCM in pairs: LCM(6,7)=42, then LCM(42,9)=126. This method scales well for more numbers. Handy when you’ve got three or more numbers to juggle.
What is the LCM of 15 and 20?
The LCM of 15 and 20 is 60 — the smallest number both 15 and 20 divide into evenly.
Prime factors: 15 = 3 × 5, 20 = 2² × 5 → LCM = 2² × 3 × 5 = 60. Or list multiples: 15 → 15, 30, 45, 60… 20 → 20, 40, 60… First common multiple is 60. That’s a common LCM in timing problems.
What is the LCM of 9 12 and 3?
The LCM of 3, 9, and 12 is 36 — the smallest number all three divide into.
Prime factors: 3 = 3, 9 = 3², 12 = 2² × 3 → LCM = 2² × 3² = 36. You can simplify by removing duplicates: since 9 and 12 already include 3, focus on 9 and 12 → LCM(9,12)=36. That’s all there is to it.
What is the LCM of 10 15 and 12?
The LCM of 10, 15, and 12 is 60 — the smallest number divisible by all three.
Prime factors: 10 = 2 × 5, 15 = 3 × 5, 12 = 2² × 3 → LCM = 2² × 3 × 5 = 60. This is a common LCM in timing problems, like when three events with different cycles coincide. Ever planned a meeting where everyone’s free? This is how you’d figure out when that happens.
