Study Guides/Maths/LCM of 93, 62 and 120 — Step-by-Step Solution
Study Guide · Maths

LCM of 93, 62 and 120

The LCM (Least Common Multiple) of 93, 62, and 120 is 3720. This is found by prime factorisation: 93 = 3 × 31; 62 = 2 × 31; 120 = 2³ × 3 × 5. The LCM takes the highest power of each prime factor: LCM = 2³ × 3 × 5 × 31 = 3720.

Question (Click to Flip)

What is the LCM of 93, 62, and 120?

Answer

The LCM of 93, 62, and 120 is 3720. Prime factorisations: 93 = 3×31, 62 = 2×31, 120 = 2³×3×5. LCM = 2³×3×5×31 = 8×3×5×31 = 3720.

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Key Facts

LCM of 93, 62, and 120 = 3720.

Prime factorisations: 93 = 3×31; 62 = 2×31; 120 = 2³×3×5.

LCM = 2³ × 3 × 5 × 31 = 3720.

Verification: 3720÷93=40 ✓; 3720÷62=60 ✓; 3720÷120=31 ✓.

31 is a prime factor common to both 93 and 62.

Step-by-Step Solution

Step 1: Prime factorise each number.

93: 93 ÷ 3 = 31 (31 is prime) 93 = 3 × 31

62: 62 ÷ 2 = 31 (31 is prime) 62 = 2 × 31

120: 120 ÷ 2 = 60 60 ÷ 2 = 30 30 ÷ 2 = 15 15 ÷ 3 = 5 5 ÷ 5 = 1 120 = 2³ × 3 × 5

Step 2: List all prime factors with their highest powers. • 2: highest power = 2³ (from 120) • 3: highest power = 3¹ (from 93 and 120) • 5: highest power = 5¹ (from 120) • 31: highest power = 31¹ (from 93 and 62)

Step 3: Multiply them. LCM = 2³ × 3 × 5 × 31 = 8 × 3 × 5 × 31 = 8 × 465 = 3720

Answer: LCM of 93, 62, and 120 = 3720

Verification

Checking that 3720 is divisible by all three numbers: • 3720 ÷ 93 = 40 ✓ • 3720 ÷ 62 = 60 ✓ • 3720 ÷ 120 = 31 ✓

All three numbers divide 3720 exactly, confirming LCM = 3720.

Also checking HCF: • HCF(93, 62) = 31 (both divisible by 31) • HCF(31, 120) = 1 (31 is prime; 120 has no factor of 31) • HCF of all three = 1

Relation: LCM × HCF = Product (for two numbers only) LCM(93, 62) = (93 × 62) / HCF(93,62) = 5766 / 31 = 186 LCM(186, 120) = ... computed as above = 3720

Questions and Answers

What is the LCM of 93, 62, and 120?+

The LCM of 93, 62, and 120 is 3720. Prime factorisations: 93 = 3×31, 62 = 2×31, 120 = 2³×3×5. LCM = 2³×3×5×31 = 8×3×5×31 = 3720.

How do you find the LCM of three numbers by prime factorisation?+

Step 1: Find prime factorisation of each number. Step 2: Take the highest power of every prime factor that appears. Step 3: Multiply them together. The result is the LCM.

What are the prime factors of 93?+

93 = 3 × 31. Both 3 and 31 are prime numbers.

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