Question

LCM of 90, 150, 1200, 300

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Answer 1

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• Write down all of the numbers as a product of their prime factors:

• Prime factorisation of 90:

2 × 3 × 3 × 5 = 2¹ × 3² × 5¹

• Prime factorisation of 150:

2 × 3 × 5 × 5 = 2¹ × 3¹ × 5²

• Prime factorisation of 1200:

2 × 2 × 2 × 2 × 3 × 5 × 5 = 2⁴ × 3¹ × 5²

• Prime factorisation of 300:

2 × 2 × 3 × 5 × 5 = 2² × 3¹ × 5²

• Find highest power of each prime number:

2⁴, 3², 5²

• Multiply these values together:

2⁴ × 3² × 5² = 3600

thus

LCM of 90, 150, 1200, 300 = 3600

Answer 2

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• Write down all of the numbers as a product of their prime factors:

• Prime factorisation of 90:

2 × 3 × 3 × 5 = 2¹ × 3² × 5¹

• Prime factorisation of 150:

2 × 3 × 5 × 5 = 2¹ × 3¹ × 5²

• Prime factorisation of 1200:

2 × 2 × 2 × 2 × 3 × 5 × 5 = 2⁴ × 3¹ × 5²

• Prime factorisation of 300:

2 × 2 × 3 × 5 × 5 = 2² × 3¹ × 5²

• Find highest power of each prime number:

2⁴, 3², 5²

• Multiply these values together:

2⁴ × 3² × 5² = 3600

thus

LCM of 90, 150, 1200, 300 = 3600